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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.06409 |
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| _version_ | 1866910198639099904 |
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| author | Cora, Gabriele Iacopetti, Alessandro Maniscalco, Lorenzo |
| author_facet | Cora, Gabriele Iacopetti, Alessandro Maniscalco, Lorenzo |
| contents | In this paper we address the existence and uniqueness of entire spacelike hypersurfaces in the Lorentz--Minkowski space $\mathbb{L}^{m+1}$ with prescribed mean curvature that are star-shaped with respect to a point and asymptotic to a light cone. We also establish a Willmore-type inequality and prove a non-existence result for spacelike radial graphs asymptotic to the light cone whose mean curvature belongs to $L^p$ for $1 \leq p\leq m$, in particular in the case of compactly supported mean curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06409 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entire spacelike radial graphs with prescribed mean curvature in the Lorentz--Minkowski space Cora, Gabriele Iacopetti, Alessandro Maniscalco, Lorenzo Analysis of PDEs 53A10, 35J66, 53C50 In this paper we address the existence and uniqueness of entire spacelike hypersurfaces in the Lorentz--Minkowski space $\mathbb{L}^{m+1}$ with prescribed mean curvature that are star-shaped with respect to a point and asymptotic to a light cone. We also establish a Willmore-type inequality and prove a non-existence result for spacelike radial graphs asymptotic to the light cone whose mean curvature belongs to $L^p$ for $1 \leq p\leq m$, in particular in the case of compactly supported mean curvature. |
| title | Entire spacelike radial graphs with prescribed mean curvature in the Lorentz--Minkowski space |
| topic | Analysis of PDEs 53A10, 35J66, 53C50 |
| url | https://arxiv.org/abs/2605.06409 |