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THALMAIER Anton

University of Luxembourg

Main Referenced Co-authors
Arnaudon, Marc (20)
Wang, Feng-Yu (11)
CHENG, Li Juan  (8)
Cheng, Li-Juan (7)
Malliavin, Paul (7)
Main Referenced Keywords
geometric flow (2); log-Sobolev inequality (2); Ricci curvature (2); Ricci flow (2); Bochner Laplacian (1);
Main Referenced Disciplines
Mathematics (72)

Publications (total 72)

The most downloaded
738 downloads
THALMAIER, A. (2016). Geometry of subelliptic diffusions. In D. Barilari, U. Boscain, ... M. Sigalotti (Eds.), Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Volume II (pp. 85-169). Zürich, Switzerland: EMS Publishing House. doi:10.4171/163 https://hdl.handle.net/10993/22438

The most cited

172 citations (OpenAlex)

Malliavin, P., & THALMAIER, A. (2006). Stochastic calculus of variations in mathematical finance. Berlin, Unknown/unspecified: Springer-Verlag. doi:10.1007/3-540-30799-0 https://hdl.handle.net/10993/13599

Cheng, L.-J., THALMAIER, A., & Wang, F.-Y. (30 September 2024). Hessian estimates for Dirichlet and Neumann eigenfunctions of Laplacian. International Mathematics Research Notices, 2024 (21), 13563-13585. doi:10.48550/arXiv.2210.09593
Peer Reviewed verified by ORBi

Cheng, L.-J., THALMAIER, A., & Wang, F.-Y. (09 October 2023). Covariant Riesz transform on differential forms for 1<p\leq2. Calculus of Variations and Partial Differential Equations, 62 (9), 245. doi:10.1007/s00526-023-02583-7
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Cheng, L.-J., & THALMAIER, A. (21 September 2023). Dimension-free Harnack inequalities for conjugate heat equations and their applications to geometric flows. Analysis and PDE, 16 (7), 1589-1620. doi:10.2140/apde.2023.16.1589
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Cheng, L.-J., THALMAIER, A., & Wang, F.-Y. (01 September 2023). Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance. Journal of Functional Analysis, 285 (5), 109997. doi:10.1016/j.jfa.2023.109997
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Chen, Q.-Q., Cheng, L.-J., & THALMAIER, A. (June 2023). Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds. Stochastic Partial Differential Equations: Analysis and Computations, 11 (2), 685-713. doi:10.1007/s40072-022-00241-1
Peer reviewed

Cheng, L.-J., THALMAIER, A., & Wang, F.-Y. (2023). Second Order Bismut formulae for Neumann semigroups on manifolds. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/52488. doi:10.48550/arXiv.2210.09607

Baudoin, F., Grong, E., Neel, R., & THALMAIER, A. (2022). Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/53331.

CHENG, L. J., Grong, E., & THALMAIER, A. (September 2021). Functional inequalities on path space of sub-Riemannian manifolds and applications. Nonlinear Analysis: Theory, Methods and Applications, 210 (112387), 1-30. doi:10.1016/j.na.2021.112387
Peer reviewed

Cao, J., Cheng, L.-J., & THALMAIER, A. (2021). Hessian heat kernel estimates and Calderón-Zygmund inequalities on complete Riemannian manifolds. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/47902.

CHENG, L. J., THALMAIER, A., & Zhang, S.-Q. (2021). Exponential contraction in Wasserstein distance on static and evolving manifolds. Revue Roumaine de Mathématiques Pures et Appliquées, 66 (1), 107-129.
Peer reviewed

Arnaudon, M., THALMAIER, A., & Wang, F.-Y. (October 2020). Gradient Estimates on Dirichlet and Neumann Eigenfunctions. International Mathematics Research Notices, 2020 (20), 7279-7305. doi:10.1093/imrn/rny208
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Baudoin, F., Grong, E., Kuwada, K., Neel, R., & THALMAIER, A. (13 August 2020). Radial processes for sub-Riemannian Brownian motions and applications. Electronic Journal of Probability, 25 (paper no. 97), 1-17. doi:10.1214/20-EJP501
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Güneysu, B., & THALMAIER, A. (28 May 2020). Scattering theory without injectivity radius assumptions, and spectral stability for the Ricci flow. Annales de l'Institut Fourier, 70 (1), 437-456. doi:10.5802/aif.3316
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THOMPSON, J., & THALMAIER, A. (May 2020). Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces. Bernoulli, 26 (3), 2202-2225. doi:10.3150/19-BEJ1190
Peer reviewed

Baudoin, F., Grong, E., Kuwada, K., & THALMAIER, A. (August 2019). Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations. Calculus of Variations and Partial Differential Equations, 58:130 (4), 1-38. doi:10.1007/s00526-019-1570-8
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Grong, E., & THALMAIER, A. (August 2019). Stochastic completeness and gradient representations for sub-Riemannian manifolds. Potential Analysis, 51 (2), 219-254. doi:10.1007/s11118-018-9710-x
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THALMAIER, A., & THOMPSON, J. (March 2019). Derivative and divergence formulae for diffusion semigroups. Annals of Probability, 47 (2), 743-773. doi:10.1214/18-AOP1269
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CHENG, L. J., THALMAIER, A., & THOMPSON, J. (November 2018). Uniform gradient estimates on manifolds with a boundary and applications. Analysis and Mathematical Physics, 8 (4), 571-588. doi:10.1007/s13324-018-0228-6
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CHENG, L. J., THALMAIER, A., & THOMPSON, J. (13 July 2018). Functional inequalities on manifolds with non-convex boundary. Science China Mathematics, 61 (8), 1421-1436. doi:10.1007/s11425-017-9344-x
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CHENG, L. J., THALMAIER, A., & THOMPSON, J. (09 May 2018). Quantitative C1-estimates by Bismut formulae. Journal of Mathematical Analysis and Applications, 465 (2), 803-813. doi:10.1016/j.jmaa.2018.05.025
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CHENG, L. J., & THALMAIER, A. (27 February 2018). Evolution systems of measures and semigroup properties on evolving manifolds. Electronic Journal of Probability, 23 (20), 1-27. doi:10.1214/18-EJP147
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CHENG, L. J., & THALMAIER, A. (15 February 2018). Spectral gap on Riemannian path space over static and evolving manifolds. Journal of Functional Analysis, 274 (4), 959-984. doi:10.1016/j.jfa.2017.12.004
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CHENG, L. J., & THALMAIER, A. (2018). Characterization of pinched Ricci curvature by functional inequalities. Journal of Geometric Analysis, 28 (3), 2312-2345. doi:10.1007/s12220-017-9905-1
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GRONG, E., & THALMAIER, A. (2016). Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part II. Mathematische Zeitschrift, 282 (1), 131-164. doi:10.1007/s00209-015-1535-3
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GRONG, E., & THALMAIER, A. (2016). Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part I. Mathematische Zeitschrift, 282 (1), 99-130. doi:10.1007/s00209-015-1534-4
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THALMAIER, A. (2016). Geometry of subelliptic diffusions. In D. Barilari, U. Boscain, ... M. Sigalotti (Eds.), Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Volume II (pp. 85-169). Zürich, Switzerland: EMS Publishing House. doi:10.4171/163
Peer reviewed

Guo, H., PHILIPOWSKI, R., & THALMAIER, A. (15 October 2015). On gradient solitons of the Ricci-Harmonic flow. Acta Mathematica Sinica, 31 (11), 1798-1804. doi:10.1007/s10114-015-4446-7
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GUO, H., PHILIPOWSKI, R., & THALMAIER, A. (September 2015). Martingales on manifolds with time-dependent connection. Journal of Theoretical Probability, 28 (3), 1038-1062. doi:10.1007/s10959-013-0536-6
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GUO, H., PHILIPOWSKI, R., & THALMAIER, A. (February 2015). An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions. Potential Analysis, 42 (2), 483-497. doi:10.1007/s11118-014-9442-5
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PHILIPOWSKI, R., & THALMAIER, A. (2015). Heat equation in vector bundles with time-dependent metric. Journal of the Mathematical Society of Japan, 67 (4), 1759-1769. doi:10.2969/jmsj/06741759
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GUO, H., PHILIPOWSKI, R., & THALMAIER, A. (November 2014). A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric. Stochastic Processes and Their Applications, 124 (11), 3535-3552. doi:10.1016/j.spa.2014.06.004
Peer reviewed

Arnaudon, M., THALMAIER, A., & Wang, F.-Y. (2014). Equivalent Harnack and gradient inequalities for pointwise curvature lower bound. Bulletin des Sciences Mathématiques, 138 (5), 643-655. doi:10.1016/j.bulsci.2013.11.001
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GUO, H., PHILIPOWSKI, R., & THALMAIER, A. (November 2013). A note on Chow's entropy functional for the Gauss curvature flow. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 351 (21-22), 833-835. doi:10.1016/j.crma.2013.10.003
Peer reviewed

GUO, H., PHILIPOWSKI, R., & THALMAIER, A. (2013). Entropy and lowest eigenvalue on evolving manifolds. Pacific Journal of Mathematics, 264 (1), 61-81. doi:10.2140/pjm.2013.264.61
Peer reviewed

Arnaudon, M., & THALMAIER, A. (2012). The differentiation of hypoelliptic diffusion semigroups. In Don Burkholder: A Collection of Articles in His Honor (pp. 497-523). University of Illinois at Urbana-Champaign.
Peer reviewed

Arnaudon, M., & THALMAIER, A. (2011). Brownian motion and negative curvature. In Random walks, boundaries and spectra (pp. 143-161). Birkhäuser/Springer Basel AG, Basel. doi:10.1007/978-3-0346-0244-0_8
Peer reviewed

Arnaudon, M., Coulibaly, K. A., & THALMAIER, A. (2011). Horizontal diffusion in C¹ path space. In Séminaire de Probabilités XLIII (pp. 73-94). Berlin, Unknown/unspecified: Springer. doi:10.1007/978-3-642-15217-7_2
Peer reviewed

THALMAIER, A. (2011). Paul Malliavin (10 September 1925 - 3 June 2010). European Mathematical Society. Newsletter, 81, 17-20. doi:10.4171/NEWS

THALMAIER, A., & Wang, F.-Y. (2011). A stochastic approach to a priori estimates and Liouville theorems for harmonic maps. Bulletin des Sciences Mathématiques, 135 (6-7), 816-843. doi:10.1016/j.bulsci.2011.07.014
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Arnaudon, M., & THALMAIER, A. (2010). Li-Yau type gradient estimates and Harnack inequalities by stochastic analysis. In Probabilistic approach to geometry (pp. 29-48). Tokyo, Japan: Math. Soc. Japan.
Peer reviewed

Arnaudon, M., & THALMAIER, A. (2010). The differentiation of hypoelliptic diffusion semigroups. Illinois Journal of Mathematics, 54 (4), 1285-1311. doi:10.1215/ijm/1348505529
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Airault, H., Malliavin, P., & THALMAIER, A. (2010). Brownian measures on Jordan-Virasoro curves associated to the Weil-Petersson metric. Journal of Functional Analysis, 259 (12), 3037-3079. doi:10.1016/j.jfa.2010.08.002
Peer reviewed

Fang, S., Luo, D., & THALMAIER, A. (2010). Stochastic differential equations with coefficients in Sobolev spaces. Journal of Functional Analysis, 259 (5), 1129-1168. doi:10.1016/j.jfa.2010.02.014
Peer reviewed

Arnaudon, M., THALMAIER, A., & Ulsamer, S. (2009). Existence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature. Mathematische Zeitschrift, 263 (2), 369-409. doi:10.1007/s00209-008-0422-6
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Arnaudon, M., THALMAIER, A., & Wang, F.-Y. (2009). Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds. Stochastic Processes and Their Applications, 119 (10), 3653-3670. doi:10.1016/j.spa.2009.07.001
Peer reviewed

Arnaudon, M., Coulibaly, K. A., & THALMAIER, A. (2008). Brownian motion with respect to a metric depending on time: definition, existence and applications to Ricci flow. Comptes Rendus. Mathématique, 346 (13-14), 773-778. doi:10.1016/j.crma.2008.05.004
Peer reviewed

Mortini, R., & THALMAIER, A. (2007). Bild von Möglichem und Unmöglichem. Luxemburger Wort, p. 16.

Arnaudon, M., Driver, B. K., & THALMAIER, A. (2007). Gradient estimates for positive harmonic functions by stochastic analysis. Stochastic Processes and Their Applications, 117 (2), 202-220. doi:10.1016/j.spa.2006.07.002
Peer reviewed

Malliavin, P., & THALMAIER, A. (2006). Stochastic calculus of variations in mathematical finance. Berlin, Unknown/unspecified: Springer-Verlag. doi:10.1007/3-540-30799-0

Arnaudon, M., THALMAIER, A., & Wang, F.-Y. (2006). Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below. Bulletin des Sciences Mathématiques, 130 (3), 223-233. doi:10.1016/j.bulsci.2005.10.001
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Airault, H., Malliavin, P., & THALMAIER, A. (2004). Canonical Brownian motion on the space of univalent functions and resolution of Beltrami equations by a continuity method along stochastic flows. Journal de Mathématiques Pures et Appliquées, 83 (8), 955-1018. doi:10.1016/j.matpur.2004.06.001
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Cruzeiro, A. B., Malliavin, P., & THALMAIER, A. (2004). Geometrization of Monte-Carlo numerical analysis of an elliptic operator: strong approximation. Comptes Rendus. Mathématique, 338 (6), 481-486. doi:10.1016/j.crma.2004.01.007
Peer reviewed

THALMAIER, A., & Wang, F.-Y. (2004). Derivative estimates of semigroups and Riesz transforms on vector bundles. Potential Analysis, 20 (2), 105-123. doi:10.1023/A:1026310604320
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Arnaudon, M., & THALMAIER, A. (2003). Yang-Mills fields and random holonomy along Brownian bridges. Annals of Probability, 31 (2), 769-790. doi:10.1214/aop/1048516535
Peer reviewed

Arnaudon, M., & THALMAIER, A. (2003). Horizontal martingales in vector bundles. In Séminaire de Probabilités XXXVI (pp. 419-456). Berlin, Germany: Springer. doi:10.1007/978-3-540-36107-7_22
Peer reviewed

Barucci, E., Malliavin, P., Mancino, M. E., Renò, R., & THALMAIER, A. (2003). The price-volatility feedback rate: an implementable mathematical indicator of market stability. Math. Finance, 13 (1), 17-35. doi:10.1111/1467-9965.t01-1-00003
Peer reviewed

Arnaudon, M., Plank, H., & THALMAIER, A. (2003). A Bismut type formula for the Hessian of heat semigroups. Comptes Rendus. Mathématique, 336 (8), 661-666. doi:10.1016/S1631-073X(03)00123-7
Peer reviewed

Malliavin, P., & THALMAIER, A. (2003). Numerical error for SDE: asymptotic expansion and hyperdistributions. Comptes Rendus. Mathématique, 336 (10), 851-856. doi:10.1016/S1631-073X(03)00189-4
Peer reviewed

Arnaudon, M., Bauer, R. O., & THALMAIER, A. (2002). A probabilistic approach to the Yang-Mills heat equation. Journal de Mathématiques Pures et Appliquées, 81 (2), 143-166. doi:10.1016/S0021-7824(02)01254-0
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Airault, H., Malliavin, P., & THALMAIER, A. (2002). Support of Virasoro unitarizing measures. Comptes Rendus. Mathématique, 335 (7), 621-626. doi:10.1016/S1631-073X(02)02539-6
Peer reviewed

Driver, B. K., & THALMAIER, A. (2001). Heat equation derivative formulas for vector bundles. Journal of Functional Analysis, 183 (1), 42-108. doi:10.1006/jfan.2001.3746
Peer reviewed

Arnaudon, M., & THALMAIER, A. (1999). Bismut type differentiation of semigroups. In Probability theory and mathematical statistics (pp. 23-32). Vilnius: TEV - Utrecht: VSP.
Peer reviewed

Arnaudon, M., Li, X.-M., & THALMAIER, A. (1999). Manifold-valued martingales, changes of probabilities, and smoothness of finely harmonic maps. Annales de l'Institut Henri Poincare (B) Probability & Statistics, 35 (6), 765-791. doi:10.1016/S0246-0203(99)00114-4
Peer reviewed

Arnaudon, M., & THALMAIER, A. (1998). Stability of stochastic differential equations in manifolds. In Séminaire de Probabilités, XXXII (pp. 188-214). Berlin, Germany: Springer. doi:10.1007/BFb0101758
Peer reviewed

THALMAIER, A. (1998). Some remarks on the heat flow for functions and forms. Electronic Communications in Probability, 3, 43-49. doi:10.1214/ECP.v3-992
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Arnaudon, M., & THALMAIER, A. (1998). Complete lifts of connections and stochastic Jacobi fields. Journal de Mathématiques Pures et Appliquées, 77 (3), 283-315. doi:10.1016/S0021-7824(98)80071-8
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THALMAIER, A., & Wang, F.-Y. (1998). Gradient estimates for harmonic functions on regular domains in Riemannian manifolds. Journal of Functional Analysis, 155 (1), 109-124. doi:10.1006/jfan.1997.3220
Peer reviewed

THALMAIER, A. (1997). On the differentiation of heat semigroups and Poisson integrals. Stochastics and Stochastics Reports, 61 (3-4), 297-321. doi:10.1080/17442509708834123
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THALMAIER, A. (1996). Martingales on Riemannian manifolds and the nonlinear heat equation. In Stochastic analysis and applications (pp. 429-440). World Sci. Publ., River Edge, NJ.
Peer reviewed

THALMAIER, A. (1996). Brownian motion and the formation of singularities in the heat flow for harmonic maps. Probability Theory and Related Fields, 105 (3), 335-367. doi:10.1007/BF01192212
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Hackenbroch, W., & THALMAIER, A. (1994). Stochastische Analysis. (Mathematische Leitfäden). Wiesbaden, Germany: Vieweg+Teubner Verlag. doi:10.1007/978-3-663-11527-4

THALMAIER, A. (1989). Asymptotik Brownscher Bewegungen im Zusammenhang mit geometrischen und potentialtheoretischen Eigenschaften Riemannscher Mannigfaltigkeiten negativer Krümmung. Regensburg, Germany: Universität Regensburg Fachbereich Mathematik.

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