A Neumann Type Maximum Principle for the Laplace Operator on Compact Riemannian Manifolds

Details A Neumann Type Maximum Principle for the Laplace Operator on Compact Riemannian Manifolds A Neumann Type Maximum Principle for the Laplace Operator on Compact Riemannian Manifolds

2007-03-16

arxiv.org/abs/math/0703505v2

Mathematics

Differential Geometry

In Theorem A, the previous maximum estimate in terms of the isoperimetric constant is replaced by a maximum estimate in terms

Scientific paper

In this paper we present a proof of a Neumann type maximum principle for the Laplace operator on compact Riemannian manifolds. A key p oint is the simple geometric nature of the constant in the a priori estimate of this maximum principle. In particular, this maximum principle can be applied to manifolds with Ricci curvature bounded from below and diameter bounded from above to yield a maximum estimate without dependence on a positive lower bound for the volume.

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