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  Covariant Riesz transform on differential forms for 1<p\leq2; Thalmaier, Anton  ; E-print/Working paper (2022) Detailed reference viewed: 62 (5 UL)Second Order Bismut formulae and applications to Neumann semigroups on manifolds; Thalmaier, Anton ; E-print/Working paper (2022) Detailed reference viewed: 29 (4 UL)Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance; Thalmaier, Anton ; E-print/Working paper (2021) For a complete connected Riemannian manifold M let V∊ C^2(M) be such that µ(dx)=exp(-V(x))vol(dx) is a probability measure on M. Taking µ as reference measure, we derive inequalities for probability ... [more ▼] For a complete connected Riemannian manifold M let V∊ C^2(M) be such that µ(dx)=exp(-V(x))vol(dx) is a probability measure on M. Taking µ as reference measure, we derive inequalities for probability measures on M linking relative entropy, Fisher information, Stein discrepancy and Wasserstein distance. These inequalities strengthen in particular the famous log-Sobolev and transportation-cost inequality and extend the so-called Entropy/Stein-discrepancy/Information (HSI) inequality established by Ledoux, Nourdin and Peccati (2015) for the standard Gaussian measure on Euclidean space to the setting of Riemannian manifolds. [less ▲] Detailed reference viewed: 72 (10 UL) Gradient Estimates on Dirichlet and Neumann Eigenfunctions; Thalmaier, Anton ; in International Mathematics Research Notices (2020), 2020(20), 7279-7305 By methods of stochastic analysis on Riemannian manifolds, we derive explicit two-sided gradient estimates for Dirichlet eigenfunctions on a d-dimensional compact Riemannian manifold D with boundary ... [more ▼] By methods of stochastic analysis on Riemannian manifolds, we derive explicit two-sided gradient estimates for Dirichlet eigenfunctions on a d-dimensional compact Riemannian manifold D with boundary. Corresponding two-sided gradient estimates for Neumann eigenfunctions are derived in the second part of the paper. [less ▲] Detailed reference viewed: 618 (112 UL)Equivalent Harnack and gradient inequalities for pointwise curvature lower bound; Thalmaier, Anton ; in Bulletin des Sciences Mathématiques (2014), 138(5), 643-655 Detailed reference viewed: 345 (32 UL)A stochastic approach to a priori estimates and Liouville theorems for harmonic mapsThalmaier, Anton ; in Bulletin des Sciences Mathématiques (2011), 135(6-7), 816-843 Nonlinear versions of Bismut type formulas for the differential of a harmonic map between Riemannian manifolds are used to establish a priori estimates for harmonic maps. A variety of Liouville type ... [more ▼] Nonlinear versions of Bismut type formulas for the differential of a harmonic map between Riemannian manifolds are used to establish a priori estimates for harmonic maps. A variety of Liouville type theorems is shown to follow as corollaries from such estimates by exhausting the domain through an increasing sequence of geodesic balls. This probabilistic method is well suited for proving sharp estimates under various curvature conditions. We discuss Liouville theorems for harmonic maps under the following conditions: small image, sublinear growth, non-positively curved targets, generalized bounded dilatation, Liouville manifolds as domains, certain asymptotic behaviour. [less ▲] Detailed reference viewed: 277 (17 UL)Gradient estimates and Harnack inequalities on non-compact Riemannian manifolds; Thalmaier, Anton ; in Stochastic Processes and Their Applications (2009), 119(10), 3653-3670 Detailed reference viewed: 276 (22 UL)Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below; Thalmaier, Anton ; in Bulletin des Sciences Mathématiques (2006), 130(3), 223-233 Detailed reference viewed: 291 (8 UL)Derivative estimates of semigroups and Riesz transforms on vector bundlesThalmaier, Anton ; in Potential Analysis (2004), 20(2), 105-123 Detailed reference viewed: 289 (27 UL)Gradient estimates for harmonic functions on regular domains in Riemannian manifoldsThalmaier, Anton ; in Journal of Functional Analysis (1998), 155(1), 109-124 Detailed reference viewed: 289 (15 UL) |
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