Comparison theorems on smooth metric measure spaces with boundary

DOI10.1515/advgeom-2016-0022zbMath1386.53041OpenAlexW2533626806WikidataQ125365910 ScholiaQ125365910MaRDI QIDQ1707366

Ze Yu Zhang, Yu Jie Zhou, Lin-Feng Wang

Publication date: 29 March 2018

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/advgeom-2016-0022

zbMATH Keywords

Dirichlet eigenvalueweighted mean curvatureBakry-Émery curvature\(\partial M\)-Jacobi fieldweighted Laplacian comparison theorem

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Gradient estimates for a nonlinear parabolic equation with Dirichlet boundary condition ⋮ Gradient estimates for weighted harmonic function with Dirichlet boundary condition ⋮ Sharp gradient estimates on weighted manifolds with compact boundary ⋮ Triviality of bounded solutions and gradient estimates for nonlinear \(f\)-heat equations on complete smooth metric measure spaces

Cites Work

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• A sharp comparison theorem for compact manifolds with mean convex boundary
• Comparison geometry for the Bakry-Emery Ricci tensor
• The upper bound of the \({{\text L}_{\mu}^2}\) spectrum
• Global heat kernel estimates
• Some geometric properties of the Bakry-Émery-Ricci tensor
• Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
• Comparison theorems for manifolds with mean convex boundary
• A general comparison theorem with applications to volume estimates for submanifolds
• Neumann Eigenvalue Estimate on a Compact Riemannian Manifold
• Extension of the Rauch Comparison Theorem to Submanifolds

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