Manifolds with Ricci curvature in the Kato class: heat kernel bounds and applications
Christian Rose, Peter Stollmann
TL;DR
This paper reviews recent advances in heat kernel estimates for manifolds with Ricci curvature in the Kato class, highlighting the impact of Kato conditions on geometric analysis and related applications.
Contribution
It summarizes new results connecting Kato class Ricci curvature conditions to heat kernel bounds and their applications.
Findings
Heat kernel bounds are established under Kato class Ricci curvature.
Kato conditions influence geometric and analytic properties of manifolds.
Applications include improved understanding of manifold heat diffusion.
Abstract
We review recent results about heat kernel estimates based on Kato conditions on the negative part of the Ricci curvature.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Mathematical Physics Problems