Stable capillary hypersurfaces supported on a horosphere in the hyperbolic space

2021 
In this paper, we study a stability problem of free boundary hypersurfaces, and also capillary ones whose boundary supported on a horosphere in hyperbolic space. We prove that umbilical hypersurfaces are only stable immersed capillary hypersurfaces whose boundary supported on a horosphere. Using the same method, we show that a totally geodesic hyperplane is only stable immersed type-II hypersurface whose boundary supported on a horosphere.
    • Correction
    • Source
    • Cite
    • Save
    • Machine Reading By IdeaReader
    29
    References
    0
    Citations
    NaN
    KQI
    []