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

2025/05/02 by López, Rafael · 1 citation
#49Q20 #53C21 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.01117

Abstract

It is proved that vertical graphs and radial graphs are strongly stable for a certain type of densities in Euclidean space \mathbb Rⁿ⁺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.

Citations

• Index and first Betti number of f-minimal hypersurfaces and self-shrinkers
• Rigidity and gap results for low index properly immersed self--shrinkers in ℝ^m+1
• Compact stable hypersurfaces with free boundary in convex solid cones with homogeneous densities
• Translating graphs by mean curvature flow
• Stable weighted minimal surfaces in manifolds with nonnegative Bakry-Emery Ricci tensor
• Stability and compactness for complete f-minimal surfaces
• Some isoperimetric problems in planes with density
• On the isoperimetric problem in Euclidean space with density
• Stability of translating solutions to mean curvature flow

Cited by

• On the first Neumann eigenvalue for critical points of a weighted area functional with asymptotically flat ends

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