On the equivalence of stochastic completeness and Liouville and Khas’minskii conditions in linear and nonlinear settings
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Publication:2847122
DOI10.1090/S0002-9947-2013-05765-0zbMath1272.31012arXiv1106.1352OpenAlexW3105769701MaRDI QIDQ2847122
Daniele Valtorta, Luciano Mari
Publication date: 4 September 2013
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1106.1352
Elliptic equations on manifolds, general theory (58J05) Diffusion processes and stochastic analysis on manifolds (58J65) Potential theory on Riemannian manifolds and other spaces (31C12) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)
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Yamabe type equations with a sign-changing nonlinearity, and the prescribed curvature problem ⋮ On the Liouville property for fully nonlinear equations with superlinear first-order terms ⋮ Drift-diffusion equations on domains in \(\mathbb{R}^d\): essential self-adjointness and stochastic completeness ⋮ Detecting the completeness of a Finsler manifold via potential theory for its infinity Laplacian ⋮ Recent rigidity results for graphs with prescribed mean curvature ⋮ Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature ⋮ Nonlinear characterizations of stochastic completeness ⋮ Some rigidity results for Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds ⋮ Liouville results for fully nonlinear equations modeled on Hörmander vector fields. II: Carnot groups and Grushin geometries ⋮ Stochastic properties of the Laplacian on Riemannian submersions ⋮ Qualitative properties of bounded subsolutions of nonlinear PDEs ⋮ Yamabe type equations with sign-changing nonlinearities on non-compact Riemannian manifolds ⋮ On the role of gradient terms in coercive quasilinear differential inequalities on Carnot groups ⋮ Mean curvature flow solitons in the presence of conformal vector fields ⋮ A splitting theorem for capillary graphs under Ricci lower bounds ⋮ Some function theoretic properties of nonlinear resistive networks
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