Maximum Principles and Consequences for $γ$-translators in $\mathbb{R}^{n+1}$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910354221563904 |
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| author | Santaella, José Torres |
| author_facet | Santaella, José Torres |
| contents | In this paper we obtain several properties of translating solitons for a general class of extrinsic geometric curvature flows given by a homogeneous, symmetric, smooth non-negative function $γ$ defined in an open cone $Γ\subset\mathbb{R}^n$. The main results are tangential principles, nonexistence theorems for closed and entire solutions, and a uniqueness result that says that any strictly convex $γ$-translator defined on a ball with a single end $\mathcal{C}^2$-asymptotic to a cylinder is the ''bowl''-type solution found in the translator paper of S. Rengaswami. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_03649 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maximum Principles and Consequences for $γ$-translators in $\mathbb{R}^{n+1}$ Santaella, José Torres Differential Geometry Analysis of PDEs In this paper we obtain several properties of translating solitons for a general class of extrinsic geometric curvature flows given by a homogeneous, symmetric, smooth non-negative function $γ$ defined in an open cone $Γ\subset\mathbb{R}^n$. The main results are tangential principles, nonexistence theorems for closed and entire solutions, and a uniqueness result that says that any strictly convex $γ$-translator defined on a ball with a single end $\mathcal{C}^2$-asymptotic to a cylinder is the ''bowl''-type solution found in the translator paper of S. Rengaswami. |
| title | Maximum Principles and Consequences for $γ$-translators in $\mathbb{R}^{n+1}$ |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2306.03649 |