TL;DR
This paper investigates the behavior of mean curvature flow on Ricci solitons, focusing on monotonic quantities related to heat-type equations on evolving submanifolds, contributing to understanding geometric flows in special ambient spaces.
Contribution
It introduces monotonic quantities for mean curvature flow within Ricci solitons, advancing the analysis of geometric flows in these special ambient spaces.
Findings
Identification of monotonic quantities in Ricci soliton backgrounds
Analysis of heat-type equations on evolving submanifolds
Foundation for future work on non-solitonic backgrounds
Abstract
We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat type equation integrated over embedded submanifolds evolving by mean curvature flow and we study their monotonicity properties. This is part of an ongoing project with Magni and Mantegazzawhich will treat the case of non-solitonic backgrounds .
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