Quantitative Stability for Minimizing Yamabe Metrics with minimal boundary
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913163878858752 |
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| author | Lin, Runze Yu, Bao |
| author_facet | Lin, Runze Yu, Bao |
| contents | In this paper, we investigate the stability of minimizing Yamabe metrics on compact manifolds with boundary, in the sense introduced by Escobar. We show that if a function nearly minimizes the Yamabe energy, then the associated conformal metric is quantitatively close to a minimizing Yamabe metric within its conformal class. Moreover, this closeness is controlled by an appropriate power of the Yamabe energy deficit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17191 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitative Stability for Minimizing Yamabe Metrics with minimal boundary Lin, Runze Yu, Bao Differential Geometry In this paper, we investigate the stability of minimizing Yamabe metrics on compact manifolds with boundary, in the sense introduced by Escobar. We show that if a function nearly minimizes the Yamabe energy, then the associated conformal metric is quantitatively close to a minimizing Yamabe metric within its conformal class. Moreover, this closeness is controlled by an appropriate power of the Yamabe energy deficit. |
| title | Quantitative Stability for Minimizing Yamabe Metrics with minimal boundary |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.17191 |