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arXiv · 2007.07017

{\L}ojasiewicz inequalities near simple bubble trees

Andrea Malchiodi·Melanie Rupflin·Ben Sharp
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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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Andrea Malchiodi, Melanie Rupflin, Ben Sharp. 2020-07-14. {\L}ojasiewicz inequalities near simple bubble trees. https://arxiv.org/abs/2007.07017

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