2008/12/31 by Efstratios Tsatis
Mathematics · Physics and Astronomy · #Context (archaeology) #Curvature #Flow (mathematics) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Heat flow #Mean curvature #Mean curvature flow #Monotonic function #Nonlinear Partial Differential Equations #Ricci flow #hep-th
paper · pdf · doi:10.1088/1751-8113/43/4/045202
published as J.Phys.A43:045202,2010 · 19 pages
openalex publication_date 2009/12/23 · arxiv created 2010/02/01 · arxiv updated 2010/02/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 the mean curvature flow and we study their monotonicity properties. This is part of an ongoing project with Magni and Mantegazza which will treat the case of non-solitonic backgrounds (arXiv:0911.5130v1).