Attaching handles to constant-mean-curvature-1 surfaces in hyperbolic 3-space

Frank Pacard; Fernando A.A. Pimentel

doi:10.1017/S147474800400012X

Attaching handles to constant-mean-curvature-1 surfaces in hyperbolic 3-space

Frank Pacard
, Fernando A.A. Pimentel

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

Abstract

Using a connected sum construction, we prove the existence of complete non-compact embedded constant-mean-curvature-1 surfaces in hyperbolic 3-space with finitely many ends and non-trivial topology. These surfaces are obtained by desingularizing finitely many mutually tangent horospheres. AMS 2000 Mathematics subject classification: Primary 53A10; 53A35.

Original language	English
Pages (from-to)	421-459
Number of pages	39
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	3
Issue number	3
DOIs	https://doi.org/10.1017/S147474800400012X
Publication status	Published - 1 Jan 2004
Externally published	Yes

Keywords

constant-mean-curvature surfaces
hyperbolic space

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10.1017/S147474800400012X

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title = "Attaching handles to constant-mean-curvature-1 surfaces in hyperbolic 3-space",

abstract = "Using a connected sum construction, we prove the existence of complete non-compact embedded constant-mean-curvature-1 surfaces in hyperbolic 3-space with finitely many ends and non-trivial topology. These surfaces are obtained by desingularizing finitely many mutually tangent horospheres. AMS 2000 Mathematics subject classification: Primary 53A10; 53A35.",

keywords = "constant-mean-curvature surfaces, hyperbolic space",

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year = "2004",

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AU - Pimentel, Fernando A.A.

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N2 - Using a connected sum construction, we prove the existence of complete non-compact embedded constant-mean-curvature-1 surfaces in hyperbolic 3-space with finitely many ends and non-trivial topology. These surfaces are obtained by desingularizing finitely many mutually tangent horospheres. AMS 2000 Mathematics subject classification: Primary 53A10; 53A35.

AB - Using a connected sum construction, we prove the existence of complete non-compact embedded constant-mean-curvature-1 surfaces in hyperbolic 3-space with finitely many ends and non-trivial topology. These surfaces are obtained by desingularizing finitely many mutually tangent horospheres. AMS 2000 Mathematics subject classification: Primary 53A10; 53A35.

KW - constant-mean-curvature surfaces

KW - hyperbolic space

U2 - 10.1017/S147474800400012X

DO - 10.1017/S147474800400012X

M3 - Article

AN - SCOPUS:85012546419

SN - 1474-7480

VL - 3

SP - 421

EP - 459

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 3

ER -

Attaching handles to constant-mean-curvature-1 surfaces in hyperbolic 3-space

Abstract

Keywords

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