Hypersurfaces with free boundary in a convex conical domain in a space form

Juncheol Pyo Annales Polonici Mathematici MSC: Primary 53C24; Secondary 49Q10. DOI: 10.4064/ap190830-27-12 Published online: 27 April 2020

Abstract

This study presents rigidity results for hypersurfaces with free boundary in a convex conical domain in a space form. Let $C$ be a conical domain with a piecewise linear boundary in a space form. A compact hypersurface with free boundary $M\subset C$ is part of a geodesic sphere if either $C$ is convex and $M$ is an embedded and has constant higher order mean curvature, or $H_l$ does not vanish and the ratio $H_r/H_{l},$ $l \lt r$, is constant on $M$.

Authors

  • Juncheol PyoDepartment of Mathematics
    Pusan National University
    Busan 46241, Republic of Korea
    and
    School of Mathematics
    Korea Institute for Advanced Study
    Seoul 02455, Republic of Korea
    e-mail

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