Evolution of the Torsional Rigidity under Geometric Flows
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910082622554112 |
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| author | Garcia, Vicent Gimeno i González-Ibáñez, Fernán |
| author_facet | Garcia, Vicent Gimeno i González-Ibáñez, Fernán |
| contents | This paper explores the behavior of the torsional rigidity of a precompact domain as the ambient manifold evolves under a geometric flow. Specifically, we derive bounds on torsional rigidity under the Ricci Flow for Heisenberg spaces and homogeneous spheres. Additionally, we establish bounds under the Inverse Mean Curvature Flow for strictly convex, free-boundary, disk-type hypersurfaces within a ball. In this latter case, by extending the analysis to the maximal existence time of the flow, we obtain inequalities of comparison with the flat disk for both volume and torsional rigidity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17435 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Evolution of the Torsional Rigidity under Geometric Flows Garcia, Vicent Gimeno i González-Ibáñez, Fernán Differential Geometry Mathematical Physics This paper explores the behavior of the torsional rigidity of a precompact domain as the ambient manifold evolves under a geometric flow. Specifically, we derive bounds on torsional rigidity under the Ricci Flow for Heisenberg spaces and homogeneous spheres. Additionally, we establish bounds under the Inverse Mean Curvature Flow for strictly convex, free-boundary, disk-type hypersurfaces within a ball. In this latter case, by extending the analysis to the maximal existence time of the flow, we obtain inequalities of comparison with the flat disk for both volume and torsional rigidity. |
| title | Evolution of the Torsional Rigidity under Geometric Flows |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2411.17435 |