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arXiv · 1803.08844

Uniform gradient estimates on manifolds with a boundary and applications

Li-Juan Cheng·Anton Thalmaier·James Thompson
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Abstract

We revisit the problem of obtaining uniform gradient estimates for Dirichlet and Neumann heat semigroups on Riemannian manifolds with boundary. As applications, we obtain isoperimetric inequalities, using Ledoux's argument, and uniform quantitative gradient estimates, firstly for $C^2_b$ functions with boundary conditions and then for the unit spectral projection operators of Dirichlet and Neumann Laplacians.

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Li-Juan Cheng, Anton Thalmaier, James Thompson. 2018-03-23. Uniform gradient estimates on manifolds with a boundary and applications. https://arxiv.org/abs/1803.08844

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