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See detailCurvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part II
Grong, Erlend UL; Thalmaier, Anton UL

in Mathematische Zeitschrift (2016), 282(1), 131-164

Using the curvature-dimension inequality proved in Part I, we look at consequences of this inequality in terms of the interaction between the sub-Riemannian geometry and the heat semi-group P_t ... [more ▼]

Using the curvature-dimension inequality proved in Part I, we look at consequences of this inequality in terms of the interaction between the sub-Riemannian geometry and the heat semi-group P_t corresponding to the sub-Laplacian. We give bounds for the gradient, entropy, a Poincaré inequality and a Li-Yau type inequality. These results require that the gradient of P_t f remains uniformly bounded whenever the gradient of f is bounded and we give several sufficient conditions for this to hold. [less ▲]

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See detailCurvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part I
Grong, Erlend UL; Thalmaier, Anton UL

in Mathematische Zeitschrift (2016), 282(1), 99-130

We give a generalized curvature-dimension inequality connecting the geometry of sub-Riemannian manifolds with the properties of its sub-Laplacian. This inequality is valid on a large class of sub ... [more ▼]

We give a generalized curvature-dimension inequality connecting the geometry of sub-Riemannian manifolds with the properties of its sub-Laplacian. This inequality is valid on a large class of sub-Riemannian manifolds obtained from Riemannian foliations. We give a geometric interpretation of the invariants involved in the inequality. Using this inequality, we obtain a lower bound for the eigenvalues of the sub-Laplacian. This inequality also lays the foundation for proving several powerful results in Part II. [less ▲]

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See detailThe Cauchy problem for D-modules on Ran spaces
Bonavolontà, Giuseppe UL

in Mathematische Zeitschrift (2015), 280(1-2), 149163

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See detailThe Lefschetz-Lunts formula for deformation quantization modules
Petit, François UL

in Mathematische Zeitschrift (2013), 273(3-4), 1119-1138

We adapt to the case of deformation quantization modules a formula of Lunts (Lefschetz fixed point theorems for Fourier–Mukai functors and DG algebras. arXiv:1102.2884. ArXiv e-prints, 2011) who ... [more ▼]

We adapt to the case of deformation quantization modules a formula of Lunts (Lefschetz fixed point theorems for Fourier–Mukai functors and DG algebras. arXiv:1102.2884. ArXiv e-prints, 2011) who calculates the trace of a kernel acting on the Hochschild homology of a DQ-algebroid. [less ▲]

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See detailNon-explosion of diffusion processes on manifolds with time-dependent metric
Kuwada, Kazumasa; Philipowski, Robert UL

in Mathematische Zeitschrift (2011), 268

We study the problem of non-explosion of diffusion processes on a manifold with time-dependent Riemannian metric. In particular we obtain that Brownian motion cannot explode in finite time if the metric ... [more ▼]

We study the problem of non-explosion of diffusion processes on a manifold with time-dependent Riemannian metric. In particular we obtain that Brownian motion cannot explode in finite time if the metric evolves under backwards Ricci flow. Our result makes it possible to remove the assumption of non-explosion in the pathwise contraction result established by Arnaudon et al. (arXiv:0904.2762, to appear in Sém. Prob.). As an important tool which is of independent interest we derive an Itô formula for the distance from a fixed reference point, generalising a result of Kendall (Ann. Prob. 15:1491–1500, 1987). [less ▲]

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See detailExistence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature
Arnaudon, Marc; Thalmaier, Anton UL; Ulsamer, Stefanie

in Mathematische Zeitschrift (2009), 263(2), 369-409

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See detailSpanning L² of a nilpotent Lie group by eigenvectors of invariant differential operators
Ludwig, Jean; Molitor-Braun, Carine UL; Scuto, Laurent

in Mathematische Zeitschrift (2008), 260(4), 717-753

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See detailWeighted Group Algebras on Groups of Polynomial Growth
Fendler, Gero; Gröchenig, Karlheinz; Leinert, Michael et al

in Mathematische Zeitschrift (2003), 245(4), 791-821

Detailed reference viewed: 45 (1 UL)