# Łojasiewicz inequalities near simple bubble trees

created by malchiodi on 15 Jul 2020

[BibTeX]

preprint

Inserted: 15 jul 2020

Year: 2020

ArXiv: 2007.07017 PDF

Abstract:

In this paper we prove a gap phenomenon for critical points of the $H$-functional on closed non-spherical surfaces when $H$ 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.

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