  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 $M_1\not=S^3$ and $M_2\not=S^3,\R\P^3$, which must
develop finite time singularity.
