Łojasiewicz--Simon inequalities near bubbling configurations for the Yamabe functional on bounded domains
Year: 2026
Type: preprint
Abstract: We establish Łojasiewicz--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.
Source: arXiv (Cornell University)
Authors: Jin, Tianling, Xiong, Jingang, Zhou, Ning
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G6591056831, G7726240407
OpenAlex ID: W7204914092