Harmonic map flow for almost-holomorphic maps
Alex Waldron (University of Wisconsin - Madison)
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.
Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php
Organizers: | Simon Blatt*, Philipp Reiter*, Armin Schikorra*, Guofang Wang |
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