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- W4300704141 abstract "We study stable constant mean curvature (CMC) hypersurfaces $Sigma$ in slabs in a product space $Mtimesr,$ where $M$ is an orientable Riemannian manifold. We obtain a characterization of stable cylinders and prove that if $Sigma$ is not a cylinder then it is locally a vertical graph. Moreover, in case $M$ is $h^n,r^n$ or $s_+^n$ and each of its boundary components is embedded then $Sigma$ is rotationally invariant. When $M$ has dimension 2 and Gaussian curvature bounded from below by a positive constant $kappa,$ we prove there is no stable CMC with free boundary connecting the boundary components of a slab of width $l>4pi/sqrt{3kappa}.$ We also show that a stable capillary surface of genus 0 in a warped product $[0,l]times_f M$ where $M=r^2, h^2$ or $s^2,$ is rotationally invariant. Finally, we prove that a stable closed CMC surface in $Mtimess^1(r),$ where $M$ is a surface with Gaussian curvature bounded from below by a positive constant $kappa$ and $s^1(r)$ the circle of radius $r,$ lifts to $Mtimesr$ provided $r>4/sqrt{3kappa}.$" @default.
- W4300704141 created "2022-10-04" @default.
- W4300704141 creator A5005900826 @default.
- W4300704141 date "2018-02-19" @default.
- W4300704141 modified "2023-09-28" @default.
- W4300704141 title "Stable constant mean curvature surfaces with free boundary in slabs" @default.
- W4300704141 doi "https://doi.org/10.48550/arxiv.1802.06848" @default.
- W4300704141 hasPublicationYear "2018" @default.
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