Existence and stability of shrinkers for the harmonic map heat flow in higher dimensions

2023/04/08 by Irfan Glogić, Glogić, Irfan, Sarah Kistner +3
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2304.04104

Abstract

We study singularity formation for the heat flow of harmonic maps from \R^d. For each d ≥ 4, we construct a compact, d-dimensional, rotationally symmetric target manifold that allows for the existence of a corotational self-similar shrinking solution (shortly shrinker) that represents a stable blowup mechanism for the corresponding Cauchy problem.

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