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Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part I Grong, Erlend ; Thalmaier, Anton 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 ▲] Detailed reference viewed: 363 (57 UL)Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: Part II Grong, Erlend ; Thalmaier, Anton 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 ▲] Detailed reference viewed: 334 (33 UL)The Cauchy problem for D-modules on Ran spaces Bonavolontà, Giuseppe in Mathematische Zeitschrift (2015), 280(1-2), 149163 Detailed reference viewed: 47 (7 UL)The Lefschetz-Lunts formula for deformation quantization modules Petit, François 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 ▲] Detailed reference viewed: 114 (2 UL)Non-explosion of diffusion processes on manifolds with time-dependent metric ; Philipowski, Robert 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 ▲] Detailed reference viewed: 123 (13 UL)Existence of non-trivial harmonic functions on Cartan-Hadamard manifolds of unbounded curvature ; Thalmaier, Anton ; in Mathematische Zeitschrift (2009), 263(2), 369-409 Detailed reference viewed: 221 (3 UL)Spanning L² of a nilpotent Lie group by eigenvectors of invariant differential operators ; Molitor-Braun, Carine ; in Mathematische Zeitschrift (2008), 260(4), 717-753 Detailed reference viewed: 118 (5 UL)Weighted Group Algebras on Groups of Polynomial Growth ; ; et al in Mathematische Zeitschrift (2003), 245(4), 791-821 Detailed reference viewed: 103 (1 UL) |
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