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arXiv · 2608.30173

{\L}ojasiewicz--Simon inequalities near bubbling configurations for the Yamabe functional on bounded domains

Tianling Jin·Jingang Xiong·Ning Zhou
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Abstract

We establish {\L}ojasiewicz--Simon type gradient inequalities for the Yamabe functional on bounded smooth domains near configurations consisting of finitely many concentrating bubbles, with or without a regular component. A weighted decomposition separates the finite-dimensional spectral and bubble parameters from an infinite-dimensional coercive remainder. We obtain quantitative estimates for the parameters, the remainder, and the corresponding energy gaps, in both the regular-plus-bubbling and the pure-bubbling regimes. These inequalities quantify the deviation from such surfaces and are essential for studying the dynamics of related parabolic flows.

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Tianling Jin, Jingang Xiong, Ning Zhou. 2026-08-31. {\L}ojasiewicz--Simon inequalities near bubbling configurations for the Yamabe functional on bounded domains. https://arxiv.org/abs/2608.30173

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