Łojasiewicz inequalities near simple bubble trees

2020/07/14 by Malchiodi, Andrea, Rupflin, Melanie, Sharp, Ben
#35R01 #53A10 #53C42 #58E30 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.07017

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.

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