Halfspace type theorems for self‐shrinkers

By M. Cavalcante, J. Espinar. 2014

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In this short paper, we extend the classical Hoffman–Meeks Halfspace Theorem [Hoffman and Meeks, ‘The strong halfspace theorem for minimal surfaces’, Invent. Math. 101 (1990) 373–377] to self‐shrinkers, that is: Let P be a hyperplane passing through the origin. The only properly immersed self‐shrinker Σ contained in one of the closed half‐space determined by P is Σ=P .

Subfields: Applied Mathematics, Geometry and Topology

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