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

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arxiv 1608.05689 v1 pith:ZCKJU3OC submitted 2016-08-19 math.DG

classification math.DG
keywords boundaryfreeminimalsurfacesballcatenoidcharacterisedcondition
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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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  1. Gap phenomena for constant mean curvature surfaces

    math.DG 2019-08 conditional novelty 6.0 of 10

    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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