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Compact stable hypersurfaces with free boundary in convex solid cones with homogeneous densities

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Abstract

We consider a smooth Euclidean solid cone endowed with a smooth homogeneous density function used to weight Euclidean volume and hypersurface area. By assuming convexity of the cone and a curvature-dimension condition, we prove that the unique compact, orientable, second order minima of the weighted area under variations preserving the weighted volume and with free boundary in the boundary of the cone are intersections with the cone of round spheres centered at the vertex.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada I, Universidad de Sevilla, 41012 , Sevilla, Spain

    Antonio Cañete

  2. Departamento de Geometría y Topología, Universidad de Granada, 18071 , Granada, Spain

    César Rosales

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  1. Antonio Cañete
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  2. César Rosales
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Correspondence to César Rosales.

Additional information

Communicated by L. Ambrosio.

A. Cañete, C. Rosales are partially supported by MCyT research project MTM2010-21206-C02-01, and Junta de Andalucía grants FQM-325 and P09-FQM-5088.

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Cañete, A., Rosales, C. Compact stable hypersurfaces with free boundary in convex solid cones with homogeneous densities. Calc. Var. 51, 887–913 (2014). https://doi.org/10.1007/s00526-013-0699-0

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