Geometric Analysis
August 16, 2021 CDT

A Liouville-type theorem for stable minimal hypersurfaces

https://doi.org/10.15781/hk9g-zz18
minimizing cones strict stability minimal hypersurfaces
ccby-4.0
Simon, Leon. 2021. “A Liouville-Type Theorem for Stable Minimal Hypersurfaces.” Ars Inveniendi Analytica, August. https://doi.org/10.15781/hk9g-zz18.

Abstract

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We prove that if M is a strictly stable complete minimal hypersurface in Euclidean space with finite density at infinity and which lies on one side of a minimal cylinder with cross-section a strictly stable area minimizing hypercone, then M must be cylindrical. Applications will be given in the references [Sim20a], [Sim20b].

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