Mean curvature flow of graphs with asymptotic Dirichlet conditions in Cartan-Hadamard manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918386396561408 |
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| author | Fernandes, Claudia de Lira, Jorge Soares, Matheus |
| author_facet | Fernandes, Claudia de Lira, Jorge Soares, Matheus |
| contents | A priori estimates for the mean curvature evolution of Killing graphs in Cartan-Hadamard manifolds with asymptotic Dirichlet conditions are established. As an application, the existence of the corresponding parabolic flow is proved, ensuring regularity of the obtained solutions through the construction of suitable barriers at points of the asymptotic boundary. Such a construction is made possible under an appropriate notion of convexity at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12548 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mean curvature flow of graphs with asymptotic Dirichlet conditions in Cartan-Hadamard manifolds Fernandes, Claudia de Lira, Jorge Soares, Matheus Differential Geometry 53E10 A priori estimates for the mean curvature evolution of Killing graphs in Cartan-Hadamard manifolds with asymptotic Dirichlet conditions are established. As an application, the existence of the corresponding parabolic flow is proved, ensuring regularity of the obtained solutions through the construction of suitable barriers at points of the asymptotic boundary. Such a construction is made possible under an appropriate notion of convexity at infinity. |
| title | Mean curvature flow of graphs with asymptotic Dirichlet conditions in Cartan-Hadamard manifolds |
| topic | Differential Geometry 53E10 |
| url | https://arxiv.org/abs/2603.12548 |