A Maximum Principle for Elliptic Pseudo-differential Operators on Closed, Riemannian Manifolds

TL;DR

This paper proves the positivity of Green's functions for a class of elliptic differential operators on closed Riemannian manifolds, extending maximum principle concepts to a geometric setting.

Contribution

It establishes a maximum principle for elliptic pseudo-differential operators on closed Riemannian manifolds, a novel extension in geometric analysis.

Findings

Green's functions are positive for the considered class of operators

Maximum principle holds for elliptic pseudo-differential operators on manifolds

Results apply to a broad class of elliptic operators on closed manifolds

Abstract

In this note we establish the positivity of Green's functions for a class of elliptic differential operators on closed, Riemannian manifolds.