Torsional Rigidity and Spherical Deficit for a Dirichlet Problem on Riemannian Manifolds
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910270312415232 |
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| author | Andrade, Maria Freitas, Allan |
| author_facet | Andrade, Maria Freitas, Allan |
| contents | In this work, we study several inequalities related to a Dirichlet problem on Riemannian manifolds whose Ricci curvature is bounded from below. First, we establish inequalities involving the torsional rigidity and discuss rigidity results characterizing metric balls in this setting. Next, we derive an integral identity associated with a Dirichlet problem, which measures the spherical deficit arising in this context. In particular, we apply this identity to the setting of Einstein manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30088 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Torsional Rigidity and Spherical Deficit for a Dirichlet Problem on Riemannian Manifolds Andrade, Maria Freitas, Allan Differential Geometry Analysis of PDEs In this work, we study several inequalities related to a Dirichlet problem on Riemannian manifolds whose Ricci curvature is bounded from below. First, we establish inequalities involving the torsional rigidity and discuss rigidity results characterizing metric balls in this setting. Next, we derive an integral identity associated with a Dirichlet problem, which measures the spherical deficit arising in this context. In particular, we apply this identity to the setting of Einstein manifolds. |
| title | Torsional Rigidity and Spherical Deficit for a Dirichlet Problem on Riemannian Manifolds |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2605.30088 |