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A family of parameter-dependent diffeomorphisms acting on function spaces over a Riemannian manifold and applications to geometric flows

  • Yuanzhen Shao
Article

Abstract

It is the purpose of this article to establish a technical tool to study regularity of solutions to parabolic equations on manifolds. As applications of this technique, we prove that solutions to the Ricci-DeTurck flow, the surface diffusion flow and the mean curvature flow enjoy joint analyticity in time and space, and solutions to the Ricci flow admit temporal analyticity.

Mathematics Subject Classification (2000)

54C35 58J99 35K55 53C44 35B65 

Keywords

Function spaces on Riemannian manifolds Regularity of solutions to parabolic equations Real analytic solutions Geometric evolution equations The Ricci flow The surface diffusion flow The mean curvature flow Maximal regularity The implicit function theorem 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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