Smooth long-time existence of Harmonic Ricci Flow on surfaces

Abstract

We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain manifold have to blow up simultaneously. As an immediate consequence, we obtain smooth long-time existence for the Harmonic Ricci Flow with large coupling constant.

29 pages, final version incorporating minor modifications based on comments from referees, to appear in J. London Math. Soc

References in corpus (3)

• Harnack Estimates for Conjugate Heat Kernel on Evolving Manifolds
• Harnack Estimates for Nonlinear Backward Heat Equations in Geometric Flows
• The (logarithmic) Sobolev inequalities along geometric flow and applications

Cited by in corpus (3)

• Horizontal curves of hyperbolic metrics
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