An integral formula for affine connections

DOI10.1007/s12220-017-9771-xzbMath1376.53032arXiv1609.01008OpenAlexW2963972227MaRDI QIDQ2411218

Yanyan Li

Publication date: 20 October 2017

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01008

zbMATH Keywords

Ricci curvatureBochner techniqueReilly's formulastatic manifold

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Linear and affine connections (53B05) Methods of local Riemannian geometry (53B21)

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Cites Work

• Unnamed Item
• Unnamed Item
• Constant mean curvature surfaces in warped product manifolds
• A Minkowski type inequality in space forms
• Minkowski formulae and Alexandrov theorems in spacetime
• Compact hypersurfaces with constant higher order mean curvatures
• Geometric applications of the solvability of Neumann problems on a Riemannian manifold
• The weighted connection and sectional curvature for manifolds with density
• Brendle's inequality on static manifolds
• An Alexandroff-Bakelman-Pucci estimate on Riemannian manifolds
• Brascamp-Lieb-type inequalities on weighted Riemannian manifolds with boundary
• An integral formula and its applications on sub-static manifolds
• On the Hessian of a function and the curvature of its graph
• A Generalization of Reilly's Formula and its Applications to a New Heintze–Karcher Type Inequality
• A general comparison theorem with applications to volume estimates for submanifolds
• A Minkowski Inequality for Hypersurfaces in the Anti‐de Sitter‐Schwarzschild Manifold
• Riemannian Geometry
• Scalar curvature deformation and a gluing construction for the Einstein constraint equations