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

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.

References in corpus (6)

• Ricci flow with surgery on three-manifolds
• Ricci Flow and the Poincare Conjecture
• Surface diffusion flow near spheres
• Anisotropic Function Spaces on Singular Manifolds
• Continuous maximal regularity on uniformly regular Riemannian manifolds
• Time-analyticity of solutions to the Ricci flow

Cited by in corpus (7)

• Some Remarks on Uniformly Regular Riemannian Manifolds
• Continuous maximal regularity on uniformly regular Riemannian manifolds
• Continuous maximal regularity on singular manifolds and its applications
• Cauchy Problems for Parabolic Equations in Sobolev-Slobodeckii and Hölder Spaces on Uniformly Regular Riemannian Manifolds
• Global existence and full convergence of the Möbius-invariant Willmore flow in the $3$-sphere
• Isometries of asymptotically conical shrinking Ricci solitons
• Functional analytic properties and regularity of the Möbius-invariant Willmore flow in ${\mathbb{R}}^n$