Analytic extensions of constant mean curvature one geometric catenoids in de Sitter 3-space

S. Fujimori; Y. Kawakami; M. Kokubu; W. Rossman; M. Umehara; K. Yamada; S. D. Yang

doi:10.1016/j.difgeo.2022.101924

Analytic extensions of constant mean curvature one geometric catenoids in de Sitter 3-space

S. Fujimori, Y. Kawakami, M. Kokubu, W. Rossman, M. Umehara, K. Yamada, S. D. Yang

Department of Mathematics

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

2 Citations (Scopus)

Abstract

We show that a certain simply-stated notion of “analytic completeness” of the image of a real analytic map implies the map admits no analytic extension. We also give a useful criterion for that notion of analytic completeness by defining arc-properness of continuous maps, which can be considered as a very weak version of properness. As an application, we judge the analytic completeness of a certain class of constant mean curvature surfaces (the so-called “G-catenoids”) or their analytic extensions in the de Sitter 3-space.

Original language	English
Article number	101924
Journal	Differential Geometry and its Application
Volume	84
DOIs	https://doi.org/10.1016/j.difgeo.2022.101924
Publication status	Published - 2022 Oct

Bibliographical note

Publisher Copyright:
© 2022 Elsevier B.V.

Keywords

Analytic completeness
Analytic extension
Constant mean curvature surface
DC-manifold
Double-cone manifold
G-catenoid

ASJC Scopus subject areas

Analysis
Geometry and Topology
Computational Theory and Mathematics

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10.1016/j.difgeo.2022.101924

Cite this

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abstract = "We show that a certain simply-stated notion of “analytic completeness” of the image of a real analytic map implies the map admits no analytic extension. We also give a useful criterion for that notion of analytic completeness by defining arc-properness of continuous maps, which can be considered as a very weak version of properness. As an application, we judge the analytic completeness of a certain class of constant mean curvature surfaces (the so-called “G-catenoids”) or their analytic extensions in the de Sitter 3-space.",

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AU - Fujimori, S.

AU - Kawakami, Y.

AU - Kokubu, M.

AU - Rossman, W.

AU - Umehara, M.

AU - Yamada, K.

AU - Yang, S. D.

PY - 2022/10

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N2 - We show that a certain simply-stated notion of “analytic completeness” of the image of a real analytic map implies the map admits no analytic extension. We also give a useful criterion for that notion of analytic completeness by defining arc-properness of continuous maps, which can be considered as a very weak version of properness. As an application, we judge the analytic completeness of a certain class of constant mean curvature surfaces (the so-called “G-catenoids”) or their analytic extensions in the de Sitter 3-space.

AB - We show that a certain simply-stated notion of “analytic completeness” of the image of a real analytic map implies the map admits no analytic extension. We also give a useful criterion for that notion of analytic completeness by defining arc-properness of continuous maps, which can be considered as a very weak version of properness. As an application, we judge the analytic completeness of a certain class of constant mean curvature surfaces (the so-called “G-catenoids”) or their analytic extensions in the de Sitter 3-space.

KW - Analytic completeness

KW - Analytic extension

KW - Constant mean curvature surface

KW - DC-manifold

KW - Double-cone manifold

KW - G-catenoid

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SN - 0926-2245

VL - 84

JO - Differential Geometry and its Application

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ER -

Analytic extensions of constant mean curvature one geometric catenoids in de Sitter 3-space

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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