On the principal eigenfunction of positive elliptic differential operators and the prescription of $Q$-curvature on closed Riemannian manifolds

TL;DR

This paper proves the non-negativity of the heat kernel for certain elliptic operators on closed Riemannian manifolds and applies this to problems involving Q-curvature in conformal geometry.

Contribution

It establishes the large time non-negativity of the heat kernel for a class of elliptic operators and connects this to Q-curvature prescription problems.

Findings

Heat kernel is non-negative for large times on closed Riemannian manifolds.

Application to Q-curvature prescription problem in conformal geometry.

Provides new insights into elliptic operators and geometric analysis.

Abstract

In this note we establish the large time non-negativity of the heat kernel for a class of elliptic differential operators on closed, Riemannian manifolds, and apply this result to a problem from conformal differential geometry.