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arXiv · 1311.3022

Homotopy classes of harmonic maps of the stratified 2-spheres and applications to geometric flows

Jingyi Chen·Yuxiang Li
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Abstract

We show that the set of harmonic maps from the 2-dimensional stratified spheres with uniformly bounded energies contains only finitely many homotopy classes. We apply this result to construct infinitely many harmonic map flows and mean curvature flows of 2-sphere in the connected sum of two closed 3-dimensional manifolds $M_1\not=S^3$ and $M_2\not=S^3,\R¶^3$, which must develop finite time singularity.

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Jingyi Chen, Yuxiang Li. 2013-11-13. Homotopy classes of harmonic maps of the stratified 2-spheres and applications to geometric flows. https://arxiv.org/abs/1311.3022

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