| Abstract | To consider convergence of a sequence of harmonic maps from surfaces, one needs to use stratified surfaces in the so-called bubble tree construction. In joint work with Yuxiang Li, we prove finiteness of homotopy classes of harmonic maps from stratified 2-spheres with uniformly bounded energies. As an application, we construct new examples of harmonic map flows and mean curvature flows which develop singularity in a finite time. |
