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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2301.09222 |
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| _version_ | 1866915517507305472 |
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| author | Tsai, Chung-Jun Tsui, Mao-Pei Wang, Mu-Tao |
| author_facet | Tsai, Chung-Jun Tsui, Mao-Pei Wang, Mu-Tao |
| contents | A new monotone quantity in graphical mean curvature flows of higher codimensions is identified in this work. The submanifold deformed by the mean curvature flow is the graph of a map between Riemannian manifolds, and the quantity is monotone increasing under the area-decreasing condition of the map. The flow provides a natural homotopy of the corresponding map and leads to sharp criteria regarding the homotopic class of maps between complex projective spaces, and maps from spheres to complex projective spaces, among others. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09222 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A New Monotone Quantity in Mean Curvature Flow Implying Sharp Homotopic Criteria Tsai, Chung-Jun Tsui, Mao-Pei Wang, Mu-Tao Differential Geometry Analysis of PDEs Geometric Topology 53C44 A new monotone quantity in graphical mean curvature flows of higher codimensions is identified in this work. The submanifold deformed by the mean curvature flow is the graph of a map between Riemannian manifolds, and the quantity is monotone increasing under the area-decreasing condition of the map. The flow provides a natural homotopy of the corresponding map and leads to sharp criteria regarding the homotopic class of maps between complex projective spaces, and maps from spheres to complex projective spaces, among others. |
| title | A New Monotone Quantity in Mean Curvature Flow Implying Sharp Homotopic Criteria |
| topic | Differential Geometry Analysis of PDEs Geometric Topology 53C44 |
| url | https://arxiv.org/abs/2301.09222 |