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

2013/11/13 by Chen, Jingyi, Li, Yuxiang
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1311.3022

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 M₁\not=S³ and M₂\not=S³,\R¶³, which must develop finite time singularity.

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