The quermassintegral inequalities for horo-convex domains in the sphere
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912762537443328 |
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| author | Pan, Shujing Scheuer, Julian |
| author_facet | Pan, Shujing Scheuer, Julian |
| contents | We study a new notion of convexity for subsets of the unit sphere, which closely resembles the horo-convexity for subsets of the hyperbolic space. We call this notion, accordingly, horo-convexity. For horo-convex hypersurfaces of the unit sphere, we prove the smooth convergence of the classical Guan/Li flow of inverse type and use this result to prove the full set of quermassintegral inequalities for horo-convex hypersurfaces of the unit sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12565 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The quermassintegral inequalities for horo-convex domains in the sphere Pan, Shujing Scheuer, Julian Differential Geometry Analysis of PDEs We study a new notion of convexity for subsets of the unit sphere, which closely resembles the horo-convexity for subsets of the hyperbolic space. We call this notion, accordingly, horo-convexity. For horo-convex hypersurfaces of the unit sphere, we prove the smooth convergence of the classical Guan/Li flow of inverse type and use this result to prove the full set of quermassintegral inequalities for horo-convex hypersurfaces of the unit sphere. |
| title | The quermassintegral inequalities for horo-convex domains in the sphere |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2512.12565 |