Periodic minimal surfaces in semidirect products

Ana Menezes

doi:10.1017/S1446788713000530

Periodic minimal surfaces in semidirect products

Ana Menezes

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

5 Scopus citations

Abstract

In this paper we prove the existence of complete minimal surfaces in some metric semidirect products. These surfaces are similar to the doubly and singly periodic Scherk minimal surfaces in R³. In particular, we obtain these surfaces in the Heisenberg space with its canonical metric, and in Sol₃ with a one-parameter family of nonisometric metrics.

Original language	English (US)
Pages (from-to)	127-144
Number of pages	18
Journal	Journal of the Australian Mathematical Society
Volume	96
Issue number	1
DOIs	https://doi.org/10.1017/S1446788713000530
State	Published - Feb 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Minimal surfaces
Semidirect products

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10.1017/S1446788713000530

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title = "Periodic minimal surfaces in semidirect products",

abstract = "In this paper we prove the existence of complete minimal surfaces in some metric semidirect products. These surfaces are similar to the doubly and singly periodic Scherk minimal surfaces in R3. In particular, we obtain these surfaces in the Heisenberg space with its canonical metric, and in Sol3 with a one-parameter family of nonisometric metrics.",

keywords = "Minimal surfaces, Semidirect products",

author = "Ana Menezes",

note = "Funding Information: The author was financially supported by CNPq-Brazil and IMPA. 02 2014 15 10 2013 96 1 127 144 14 01 2013 14 01 2013 Copyright {\textcopyright}2013 Australian Mathematical Publishing Association Inc. 2013 Australian Mathematical Publishing Association Inc. ",

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N2 - In this paper we prove the existence of complete minimal surfaces in some metric semidirect products. These surfaces are similar to the doubly and singly periodic Scherk minimal surfaces in R3. In particular, we obtain these surfaces in the Heisenberg space with its canonical metric, and in Sol3 with a one-parameter family of nonisometric metrics.

AB - In this paper we prove the existence of complete minimal surfaces in some metric semidirect products. These surfaces are similar to the doubly and singly periodic Scherk minimal surfaces in R3. In particular, we obtain these surfaces in the Heisenberg space with its canonical metric, and in Sol3 with a one-parameter family of nonisometric metrics.

KW - Minimal surfaces

KW - Semidirect products

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Periodic minimal surfaces in semidirect products

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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