Łojasiewicz inequalities near simple bubble trees
arXiv:2007.07017
Abstract
In this paper we prove a gap phenomenon for critical points of the -functional on closed non-spherical surfaces when is constant, and in this setting furthermore prove that sequences of almost critical points satisfy Łojasiewicz inequalities as they approach the first non-trivial bubble tree. To prove these results we derive sufficient conditions for Łojasiewicz inequalities to hold near a finite-dimensional submanifold of almost-critical points for suitable functionals on a Hilbert space.
29 pages. Minor typos corrected and references updated. To appear in Amer. J. Math