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.
Fontana, L., Morpurgo, C., Qin, L. (2026). Sharp Estimates and Inequalities on Riemannian Manifolds with Euclidean Volume Growth. THE JOURNAL OF GEOMETRIC ANALYSIS, 36(5) [10.1007/s12220-026-02364-6].
Sharp Estimates and Inequalities on Riemannian Manifolds with Euclidean Volume Growth
Fontana L.;
2026
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.
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