A Neumann Type Maximum Principle for the Laplace Operator on Compact Riemannian Manifolds
Abstract
Description
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.
In Theorem A, the previous maximum estimate in terms of the isoperimetric constant is replaced by a maximum estimate in terms of the volume-normalized isoperimetric constant. The statements of Gallot's estimate for the isoperimetric constant are corrected
In Theorem A, the previous maximum estimate in terms of the isoperimetric constant is replaced by a maximum estimate in terms of the volume-normalized isoperimetric constant. The statements of Gallot's estimate for the isoperimetric constant are corrected