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A gap theorem for free boundary minimal surfaces in the three-ball

· 2016 · math.DG · arXiv 1608.05689

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abstract

We show that, among free boundary minimal surfaces in the unit ball in the three-dimensional Euclidean space, the flat equatorial disk and the critical catenoid are characterised by a pinching condition on the length of their second fundamental form.

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math.DG 1

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2019 1

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CONDITIONAL 1

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Gap phenomena for constant mean curvature surfaces

math.DG · 2019-08-26 · conditional · novelty 6.0

A free boundary CMC surface in the 3-ball with traceless second fundamental form pinched by (2+H<x,N>)^2/2 is a spherical cap or a Delaunay annulus.

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  • Gap phenomena for constant mean curvature surfaces math.DG · 2019-08-26 · conditional · none · ref 2 · internal anchor

    A free boundary CMC surface in the 3-ball with traceless second fundamental form pinched by (2+H<x,N>)^2/2 is a spherical cap or a Delaunay annulus.