Sharp estimates of the spherical heat kernel
Adam Nowak, Peter Sj\"ogren, Tomasz Z. Szarek
TL;DR
This paper provides precise two-sided estimates for the heat kernel on spheres of any dimension, resolving a long-standing open problem in geometric analysis.
Contribution
It offers the first sharp, comprehensive bounds for the spherical heat kernel across all dimensions, advancing understanding in geometric analysis and heat kernel estimates.
Findings
Established sharp two-sided bounds for the spherical heat kernel
Solved a long-standing open problem in geometric analysis
Provides tools for further research in heat kernel estimates on manifolds
Abstract
We prove sharp two-sided global estimates for the heat kernel associated with a Euclidean sphere of arbitrary dimension. This solves a long-standing open problem.
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