Remarks on the generalised Calabi-Yau problem in higher codimension
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910409486761984 |
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| author | Assimos, Renan Békési, Balázs Márk Gentile, Giuseppe |
| author_facet | Assimos, Renan Békési, Balázs Márk Gentile, Giuseppe |
| contents | By introducing a more flexible notion of convexity, we obtain a new Omori-Yau maximum principle for harmonic maps. In the spirit of the Calabi-Yau conjectures, this principle is more suitable for studying the unboundedness of certain totally geodesic projections of minimal submanifolds of higher codimension. We further explore this maximum principle by applying it to conformal maps, harmonic maps into Cartan-Hadamard manifolds, as well as cone, wedge and halfspace theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remarks on the generalised Calabi-Yau problem in higher codimension Assimos, Renan Békési, Balázs Márk Gentile, Giuseppe Differential Geometry 53C43, 58J65, 53C42, 53A10 By introducing a more flexible notion of convexity, we obtain a new Omori-Yau maximum principle for harmonic maps. In the spirit of the Calabi-Yau conjectures, this principle is more suitable for studying the unboundedness of certain totally geodesic projections of minimal submanifolds of higher codimension. We further explore this maximum principle by applying it to conformal maps, harmonic maps into Cartan-Hadamard manifolds, as well as cone, wedge and halfspace theorems. |
| title | Remarks on the generalised Calabi-Yau problem in higher codimension |
| topic | Differential Geometry 53C43, 58J65, 53C42, 53A10 |
| url | https://arxiv.org/abs/2404.08781 |