Rigidity of contracting map using harmonic map heat flow
Date:
In this talk, we are going to consider the rigidity of map between possibly curved closed manifolds, which is motivated by the recent work of Tsai-Tsui-Wang. We show that distance non-increasing map between complex projective spaces is either an isometry or homotopically trivial. 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 and it partially solves a Conjecture of Tsai-Tsui-Wang. References: [Rigidity of contracting map using harmonic map heat flow](https://arxiv.org/abs/2306.12258)
