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 [10]). We present an alternative and unified proof of the Chern-Osserman inequality satisfied by these minimal surfaces (in ℝn and in ℕn(b)), based in the isoperimetric analysis mentioned above. 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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Supported by the Fundació Caixa Castelló-Bancaixa Grants P1.1B2006-34 and P1.1B2009-14.
Supported by MICINN grant No. MTM2010-21206-C02-02.
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Gimeno, V., Palmer, V. Extrinsic isoperimetry and compactification of minimal surfaces in Euclidean and hyperbolic spaces. Isr. J. Math. 194, 539–553 (2013). https://doi.org/10.1007/s11856-012-0100-6
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DOI: https://doi.org/10.1007/s11856-012-0100-6