What question did this study set out to answer?

The aim is to provide sharp estimates for heat kernels and Green's functions on specific Riemannian manifolds.

Sharp Estimates and Inequalities on Riemannian Manifolds with Euclidean Volume Growth

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This analysis reveals sharp inequalities in noncompact Riemannian manifolds, indicating new mathematical insights.

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

Fontana et al. (2026) studied this question.

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