A Costa-Hoffman-Meeks type surface in ℍ²×ℝ

Morabito, Filippo

doi:10.1090/S0002-9947-2010-04952-9

A Costa-Hoffman-Meeks type surface in ${\mathbb H^2 \times \mathbb R }$
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Trans. Amer. Math. Soc. 363 (2011), 1-36 Request permission

Abstract:

We show the existence in the space ${\mathbb H}^2 \times \mathbb {R}$ of a family of embedded minimal surfaces of genus $1\leqslant k<+\infty$ and finite total extrinsic curvature with two catenoidal type ends and one middle planar end. The proof is based on a gluing procedure.

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