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arXiv · 1011.5380

Extrinsic isoperimetry and compactification of minimal surfaces in Euclidean and Hyperbolic spaces

Vicent Gimeno·Vicente Palmer
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Abstract

We study the topology of (properly) immersed complete minimal surfaces $P^2$ in Hyperbolic and Euclidean spaces which have finite total extrinsic curvature, using some isoperimetric inequalities satisfied by the extrinsic balls in these surfaces, (see \cite{Pa}). We present an alternative and partially unified proof of the Chern-Osserman inequality satisfied by these minimal surfaces, (in $\erre^n$ and in $\Han$), based in the isoperimetric analysis above alluded. Finally, we show a Chern-Osserman type equality attained by complete minimal surfaces in the Hyperbolic space with finite total extrinsic curvature.

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Vicent Gimeno, Vicente Palmer. 2010-11-24. Extrinsic isoperimetry and compactification of minimal surfaces in Euclidean and Hyperbolic spaces. https://arxiv.org/abs/1011.5380

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