Compact anisotropic stable hypersurfaces with free boundary in convex solid cones

César Rosales

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arXiv · 2302.06538

Compact anisotropic stable hypersurfaces with free boundary in convex solid cones

César Rosales

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Abstract

We consider a convex solid cone $\mathcal{C}\subset\mathbb{R}^{n+1}$ with vertex at the origin and boundary $\partial\mathcal{C}$ smooth away from $0$. Our main result shows that a compact two-sided hypersurface $\Sigma$ immersed in $\mathcal{C}$ with free boundary in $\partial\mathcal{C}\setminus\{0\}$ and minimizing, up to second order, an anisotropic area functional under a volume constraint is contained in a Wulff-shape.

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BibTeX RIS

César Rosales. 2023-02-13. Compact anisotropic stable hypersurfaces with free boundary in convex solid cones. https://arxiv.org/abs/2302.06538

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