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arXiv · 2505.01117

Stability of vertical and radial graphs in the Euclidean space with density

Rafael López
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Abstract

It is proved that vertical graphs and radial graphs are strongly stable for a certain type of densities in Euclidean space ${\mathbb R}^{n+1}$. Particular cases of these densities include translators, expanders and singular minimal hypersurfaces. Using techniques of calibrations, it is also proved that for densities depending on a spatial coordinate, stationary vertical graphs are weighted minimizers in a certain class of hypersurfaces.

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Rafael López. 2025-05-02. Stability of vertical and radial graphs in the Euclidean space with density. https://arxiv.org/abs/2505.01117

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