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{\L}ojasiewicz inequalities near simple bubble trees
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.Comment: 29 page
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