Harmonic map flow for almost-holomorphic maps

Alex Waldron (University of Wisconsin - Madison)

10-Aug-2021, 17:00-18:00 (3 years ago)

Abstract: I'll describe some history, recent results, and open problems about harmonic map flow in dimension two.

The main result is as follows: let $\Sigma$ be a compact oriented surface and $N$ a compact Kähler manifold with nonnegative holomorphic bisectional curvature (e.g. $\mathbb{CP}^n$). For harmonic map flow starting from an almost-holomorphic map $\Sigma \to N$ (in the energy sense), the ``body map'' at each singular time is continuous, and no ``neck'' appears between the body map and the bubble tree.

This is joint work with Chong Song.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the discipline

( paper )


Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

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Organizers: Simon Blatt*, Philipp Reiter*, Armin Schikorra*, Guofang Wang
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