Continuous maximal regularity on uniformly regular Riemannian manifolds

Abstract

We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show that solutions to the Yamabe flow instantaneously regularize and become real analytic in space and time. The regularity result is obtained by introducing a family of parameter-dependent diffeomorphims acting on functions over Riemannian manifolds in conjunction with maximal regularity and the implicit function theorem.

References in corpus (2)

• Anisotropic Function Spaces on Singular Manifolds
• A family of parameter-dependent diffeomorphisms acting on function spaces over a Riemannian manifold and applications to geometric flows

Cited by in corpus (11)

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• Cauchy Problems for Parabolic Equations in Sobolev-Slobodeckii and Hölder Spaces on Uniformly Regular Riemannian Manifolds
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• Global existence and full convergence of the Möbius-invariant Willmore flow in the $3$-sphere
• Functional analytic properties and regularity of the Möbius-invariant Willmore flow in ${\mathbb{R}}^n$
• Function Spaces on Uniformly Regular and Singular Riemannian Manifolds