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arxiv: 1803.05737 · v1 · pith:ORGCLMXDnew · submitted 2018-03-15 · 🧮 math.DG

Blowup criteria for geometric flows on surfaces

Lothar Schiemanowski This is my paper
classification 🧮 math.DG
keywords surfacescriteriaflowsgeometricblowflowproveblowup
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Utilizing a splitting of geometric flows on surfaces introduced by Buzano and Rupflin, we present a general scheme to prove blow up criteria for such geometric flows. A vital ingredient is a new compactness theorem for families of metrics on surfaces with a uniform bound on their volumes, square integrals of their curvatures and injectivity radii. In particular we prove blow up criteria for the harmonic Ricci flow and for the spinor flow on surfaces.

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  1. Regularity estimates for the gradient flow of a spinorial energy functional

    math.DG 2019-06 unverdicted novelty 6.0

    Regularity estimates prove that blow-up of the second covariant derivative of the spinor is the sole obstruction to long-time existence of the spinor flow, generalizing surface criteria to higher dimensions.