Slab theorem and halfspace theorem for constant mean curvature surfaces in H2 X R

Laurent Hauswirth; Ana Menezes; Magdalena Rodríguez

doi:10.4171/RMI/1372

Slab theorem and halfspace theorem for constant mean curvature surfaces in H² X R

Laurent Hauswirth, Ana Menezes, Magdalena Rodríguez

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove that a properly embedded annular end of a surface in H² X R with constant mean curvature 0 < H ≤ 1=2 can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature 0 < H ≤ 1=2 contained in H² X Œ0; C1/ and with finite topology is necessarily a graph over a simply connected domain of H². For the case H D 1=2, the graph is entire.

Original language	English (US)
Pages (from-to)	307-320
Number of pages	14
Journal	Revista Matematica Iberoamericana
Volume	39
Issue number	1
DOIs	https://doi.org/10.4171/RMI/1372
State	Published - 2023

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Constant mean curvature surface
halfspace theorem
slab theorem

Access to Document

10.4171/RMI/1372

Cite this

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AU - Menezes, Ana

AU - Rodríguez, Magdalena

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N2 - We prove that a properly embedded annular end of a surface in H2 X R with constant mean curvature 0 < H ≤ 1=2 can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature 0 < H ≤ 1=2 contained in H2 X Œ0; C1/ and with finite topology is necessarily a graph over a simply connected domain of H2. For the case H D 1=2, the graph is entire.

AB - We prove that a properly embedded annular end of a surface in H2 X R with constant mean curvature 0 < H ≤ 1=2 can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature 0 < H ≤ 1=2 contained in H2 X Œ0; C1/ and with finite topology is necessarily a graph over a simply connected domain of H2. For the case H D 1=2, the graph is entire.

KW - Constant mean curvature surface

KW - halfspace theorem

KW - slab theorem

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