Sharp Estimates and Inequalities on Riemannian Manifolds with Euclidean Volume Growth

Key Points

• The aim is to provide sharp estimates for heat kernels and Green's functions on specific Riemannian manifolds.
• Analyzed complete noncompact Riemannian manifolds
• Focused on manifolds with Euclidean volume growth
• Investigated nonnegative Ricci curvature
• Applied findings to derive Moser-Trudinger inequalities
• Estimates for heat kernels and Green's functions were successfully obtained
• Demonstrated sharp Moser-Trudinger inequalities
• Findings enhance the understanding of geometric analysis in Riemannian contexts