{\L}ojasiewicz inequalities near simple bubble trees
Analysis of PDEs
2023-04-24 v2 Differential Geometry
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 {\L}ojasiewicz inequalities as they approach the first non-trivial bubble tree. To prove these results we derive sufficient conditions for {\L}ojasiewicz inequalities to hold near a finite-dimensional submanifold of almost-critical points for suitable functionals on a Hilbert space.
Cite
@article{arxiv.2007.07017,
title = {{\L}ojasiewicz inequalities near simple bubble trees},
author = {Andrea Malchiodi and Melanie Rupflin and Ben Sharp},
journal= {arXiv preprint arXiv:2007.07017},
year = {2023}
}
Comments
29 pages. Minor typos corrected and references updated. To appear in Amer. J. Math