Curvature Deformations on Complete Manifolds with Boundary
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916571936456704 |
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| author | Cruz, Tiarlos Santos, Almir Silva |
| author_facet | Cruz, Tiarlos Santos, Almir Silva |
| contents | This paper investigates conformal deformations of the scalar curvature and mean curvature on complete Riemannian manifolds with boundary. We establish sufficient conditions for the existence of conformal deformations to complete metrics with positive scalar curvature and mean convex boundary. Building upon these results, we explore further deformation scenarios, including those that increase the mean curvature. Finally, we consider the case of deforming complete manifolds with negative scalar curvature on manifolds with noncompact boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Curvature Deformations on Complete Manifolds with Boundary Cruz, Tiarlos Santos, Almir Silva Differential Geometry This paper investigates conformal deformations of the scalar curvature and mean curvature on complete Riemannian manifolds with boundary. We establish sufficient conditions for the existence of conformal deformations to complete metrics with positive scalar curvature and mean convex boundary. Building upon these results, we explore further deformation scenarios, including those that increase the mean curvature. Finally, we consider the case of deforming complete manifolds with negative scalar curvature on manifolds with noncompact boundary. |
| title | Curvature Deformations on Complete Manifolds with Boundary |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2501.10855 |