Year: 2020
Type: preprint
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 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.
Source: arXiv (Cornell University)
Authors: Malchiodi, Andrea, Rupflin, Melanie, Sharp, Ben
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7074021129