The uniqueness of minimal maps into Cartan-Hadamard manifolds via the squared singular values
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915169729249280 |
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| author | Jia, Zhiwei Li, Minghao Yang, Ling |
| author_facet | Jia, Zhiwei Li, Minghao Yang, Ling |
| contents | In this paper, we give a uniqueness theorem for the Dirichlet problem of minimal maps into general Riemannian manifolds with non-positive sectional curvature, improving Theorem 5.2 of Lee-Ooi-Tsui's paper published in J. Geom. Anal.. The proof of this theorem is based on the convexity of several functions in terms of squared singular values along the geodesic homotopy of two given minimal maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16968 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The uniqueness of minimal maps into Cartan-Hadamard manifolds via the squared singular values Jia, Zhiwei Li, Minghao Yang, Ling Differential Geometry In this paper, we give a uniqueness theorem for the Dirichlet problem of minimal maps into general Riemannian manifolds with non-positive sectional curvature, improving Theorem 5.2 of Lee-Ooi-Tsui's paper published in J. Geom. Anal.. The proof of this theorem is based on the convexity of several functions in terms of squared singular values along the geodesic homotopy of two given minimal maps. |
| title | The uniqueness of minimal maps into Cartan-Hadamard manifolds via the squared singular values |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2502.16968 |