Rigidity of contracting map using harmonic map heat flow

Author:

Man-Chun Lee, Jingbo Wan

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Analysis of PDEs (math.AP), Geometric Topology (math.GT)

journal:

date:

2023-06-20 16:00:00

Abstract

Motivated by the recent work of Tsai-Tsui-Wang, we consider the rigidity of map between compact manifolds with positive curvature. We show that distance non-increasing map between complex projective spaces is either an isometry or homotopically trivial, which partially solves a question of Tsai-Tsui-Wang about weakly contracting maps. The rigidity result also holds on a wider class of manifolds with positive curvature and weaker contracting property on the map in between distance non-increasing and area non-increasing. This is based on the harmonic map heat flow.

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