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Łojasiewicz--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 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.

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Cite

BibTeXRIS
BibTeX
@misc{jin2026łojasiewiczsimon,
  title = {{Łojasiewicz--Simon inequalities near bubbling configurations for the Yamabe functional on bounded domains}},
  author = {Tianling Jin and Jingang Xiong and Ning Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30173},
  eprint = {2608.30173},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30173},
}
RIS
TY  - UNPB
TI  - Łojasiewicz--Simon inequalities near bubbling configurations for the Yamabe functional on bounded domains
AU  - Tianling Jin
AU  - Jingang Xiong
AU  - Ning Zhou
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30173
UR  - https://arxiv.org/abs/2608.30173
AB  - 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.
ER  -