Ricci expanders and type III Ricci flow
Li Ma
TL;DR
This paper explores the derivation of Ricci expanders from W+-functionals using heat kernel estimates related to type III Ricci flow singularities, extending previous work on type I flows.
Contribution
It introduces new heat kernel bounds for type III Ricci flow, connecting Ricci expanders with conjugate heat equations and W+-functionals.
Findings
Established Gaussian bounds for heat kernels in type III Ricci flow
Connected Ricci expanders with conjugate heat equations
Extended Cao-Zhang's work to type III singularities
Abstract
In this paper, we study how to get the Ricci expanders from W+-functional through the heat kernel estimate of the conjugate heat equation to the type III singularity of Ricci flow. The Gaussian upper and lower bounds are established for the related heat kernel in accordance to the interesting work of Cao-Zhang for the type I Rici flow.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research