Locally constrained flows and geometric inequalities in sphere
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916197189025792 |
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| author | Ding, Shanwei Li, Guanghan |
| author_facet | Ding, Shanwei Li, Guanghan |
| contents | In this paper, we uncover an intriguing algebra property of an element symmetric polynomial. By this property, we establish the longtime existence and convergence of a locally constrained flow, thereby some families of geometric inequalities in sphere can be derived. Meanwhile, a new family of ``three terms'' geometric inequalities involving two weighted curvature integrals and one quermassintegral are proved. Unlike hyperbolic spaces, we also obtain an inverse weighted geometric inequality in sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07281 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Locally constrained flows and geometric inequalities in sphere Ding, Shanwei Li, Guanghan Differential Geometry Analysis of PDEs In this paper, we uncover an intriguing algebra property of an element symmetric polynomial. By this property, we establish the longtime existence and convergence of a locally constrained flow, thereby some families of geometric inequalities in sphere can be derived. Meanwhile, a new family of ``three terms'' geometric inequalities involving two weighted curvature integrals and one quermassintegral are proved. Unlike hyperbolic spaces, we also obtain an inverse weighted geometric inequality in sphere. |
| title | Locally constrained flows and geometric inequalities in sphere |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2403.07281 |