The equality case in Cheeger's and Buser's inequalities on RCD spaces
We prove that the sharp Buser’s inequality obtained in the framework of RCD(1, ∞) spaces by the first two authors [29] is rigid, i.e. equality is obtained if and only if the space splits isomorphically a Gaussian. The result is new even in the smooth setting. We also show that the equality in Cheege...
| Autores principales: | , , |
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| Formato: | Journal article |
| Lenguaje: | English |
| Publicado: |
Elsevier
2021
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| Sumario: | We prove that the sharp Buser’s inequality obtained in the framework of RCD(1, ∞) spaces by the first two authors [29] is rigid, i.e. equality is obtained if and only if the space splits isomorphically a Gaussian. The result is new even in the smooth setting. We also show that the equality in Cheeger’s inequality is never attained in the setting of RCD(K, ∞) spaces with finite diameter or positive curvature, and we provide several examples of spaces with Ricci curvature bounded below where these assumptions are not satisfied and the equality is attained. |
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