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

doi:10.1007/s00030-014-0275-0

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

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Publication date: 2013-09-09

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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.