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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2401.14097 |
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- In this paper, we establish the existence of prescribed mean curvature (PMC) hypersurfaces in conformal product manifolds with (possibly empty) $C^{1,α}$ fixed graphical boundaries under a barrier condition. This result generalizes Gerhardt's work to non-flat conformal backgrounds. As a consequence, we obtain new solutions to the high-dimensional PMC Plateau problem with explicitly characterized topology. Moreover, under a quasi-decreasing condition on the PMC function, we demonstrate that the resulting hypersurfaces are $C^1$ graphs.