The Yamabe flow on incomplete manifolds

Abstract

This article is concerned with developing an analytic theory for second order nonlinear parabolic equations on singular manifolds. Existence and uniqueness of solutions in an Lp-framework is established by maximal regularity tools. These techniques are applied to the Yamabe flow. It is proven that the Yamabe flow admits a unique local solution within a class of incomplete initial metrics.

arXiv admin note: text overlap with arXiv:1502.06696

References in corpus (3)

• Ricci Flow in Two Dimensions
• Anisotropic Function Spaces on Singular Manifolds
• Singular parabolic equations of second order on manifolds with singularities

Cited by in corpus (5)

• Singular parabolic equations of second order on manifolds with singularities
• Wellposedness of a nonlocal nonlinear diffusion equation of image processing
• Function Spaces on Uniformly Regular and Singular Riemannian Manifolds
• Generalized Yamabe Flows
• Degenerate parabolic $p$-Laplacian equations: existence, uniqueness and asymptotic behavior of solutions