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Spring 2014 Constant mean curvature $k$-noids in homogeneous manifolds
Julia Plehnert
Illinois J. Math. 58(1): 233-249 (Spring 2014). DOI: 10.1215/ijm/1427897176

Abstract

For each $k\geq2$, we construct a family of surfaces in $\Sigma(\kappa)\times\mathbb{R}$ with constant mean curvature $H\in[0,1/2]$, where $\kappa+4H^{2}\leq0$ and $\Sigma(\kappa)$ is a two-dimensional space form. The surfaces are invariant under $2\pi/k$-rotations about a vertical fiber of $\Sigma(\kappa)\times\mathbb{R}$, have genus zero, and $2k$ ends. Each surface arises as the sister surface of a minimal graph in a homogeneous $3$-manifold. The domain of the graph is non-convex. We use the sisters of a generalization of Jorge–Meeks-$k$-noids in homogeneous $3$-manifolds as barriers in the conjugate Plateau construction.

Citation

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Julia Plehnert. "Constant mean curvature $k$-noids in homogeneous manifolds." Illinois J. Math. 58 (1) 233 - 249, Spring 2014. https://doi.org/10.1215/ijm/1427897176

Information

Published: Spring 2014
First available in Project Euclid: 1 April 2015

zbMATH: 1314.53109
MathSciNet: MR3331849
Digital Object Identifier: 10.1215/ijm/1427897176

Subjects:
Primary: 53A10, 53C30

Rights: Copyright © 2014 University of Illinois at Urbana-Champaign

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Vol.58 • No. 1 • Spring 2014
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