Lipschitz regularity of harmonic map heat flows from $\mathrm{RCD}$ spaces into $\mathrm{CAT}(0)$ spaces

Bang-Xian Han, Hui-Chun Zhang, Xi-Ping Zhu

We prove positive-time regularity for harmonic map heat flows from finite-dimensional $\mathrm{RCD}(K,N)$ spaces into complete $\mathrm{CAT}(0)$ spaces, without assuming that eithe…