Liouville Theorems on pseudohermitian manifolds with nonnegative Tanaka-Webster curvature
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910740451950592 |
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| author | Catino, Giovanni Monticelli, Dario Daniele Roncoroni, Alberto Wang, Xiaodong |
| author_facet | Catino, Giovanni Monticelli, Dario Daniele Roncoroni, Alberto Wang, Xiaodong |
| contents | In this paper we study positive solutions to the CR Yamabe equation in noncompact $(2n+1)$-dimensional Sasakian manifolds with nonnegative curvature. In particular, we show that the Heisenberg group $\mathbb{H}^1$ is the only (complete) Sasakian space with nonnegative Tanaka-Webster scalar curvature admitting a (nontrivial) positive solution. Moreover, under some natural assumptions, we prove this strong rigidity result in higher dimensions, extending the celebrated Jerison-Lee's result to curved manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08500 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Liouville Theorems on pseudohermitian manifolds with nonnegative Tanaka-Webster curvature Catino, Giovanni Monticelli, Dario Daniele Roncoroni, Alberto Wang, Xiaodong Differential Geometry Analysis of PDEs In this paper we study positive solutions to the CR Yamabe equation in noncompact $(2n+1)$-dimensional Sasakian manifolds with nonnegative curvature. In particular, we show that the Heisenberg group $\mathbb{H}^1$ is the only (complete) Sasakian space with nonnegative Tanaka-Webster scalar curvature admitting a (nontrivial) positive solution. Moreover, under some natural assumptions, we prove this strong rigidity result in higher dimensions, extending the celebrated Jerison-Lee's result to curved manifolds. |
| title | Liouville Theorems on pseudohermitian manifolds with nonnegative Tanaka-Webster curvature |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2412.08500 |