An area bound for surfaces in Riemannian manifolds
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
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| _version_ | 1866913671845773312 |
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| author | Bangert, Victor Kuwert, Ernst |
| author_facet | Bangert, Victor Kuwert, Ernst |
| contents | Let $M$ be a compact Riemannian manifold not containing any totally geodesic surface. Our main result shows that then the area of any complete surface immersed into $M$ is bounded by a multiple of its extrinsic curvature energy, i.e. by a multiple of the integral of the squared norm of its second fundamental form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_03457 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | An area bound for surfaces in Riemannian manifolds Bangert, Victor Kuwert, Ernst Differential Geometry 53C42, 49Q10, 58E35 Let $M$ be a compact Riemannian manifold not containing any totally geodesic surface. Our main result shows that then the area of any complete surface immersed into $M$ is bounded by a multiple of its extrinsic curvature energy, i.e. by a multiple of the integral of the squared norm of its second fundamental form. |
| title | An area bound for surfaces in Riemannian manifolds |
| topic | Differential Geometry 53C42, 49Q10, 58E35 |
| url | https://arxiv.org/abs/1907.03457 |