Sharp estimates and inequalities on Riemannian manifolds with Euclidean volume growth

TL;DR

This paper derives precise estimates for heat kernels and Green's functions on certain Riemannian manifolds, and applies these to establish optimal Moser-Trudinger inequalities, advancing understanding of geometric analysis on these spaces.

Contribution

It provides sharp heat kernel and Green's function estimates on manifolds with Euclidean volume growth and nonnegative Ricci curvature, and uses these to prove optimal inequalities.

Findings

Sharp heat kernel estimates on specified manifolds

Precise Green's function bounds

Optimal Moser-Trudinger inequalities established

Abstract

We obtain sharp estimates for heat kernels and Green's functions on complete noncompact Riemannian manifolds with Euclidean volume growth and nonnegative Ricci curvature. We will then apply these estimates to obtain sharp Moser-Trudinger inequalities on such manifolds.