Osaka Journal of Mathematics

Analytic extension of Jorge-Meeks type maximal surfaces in Lorentz-Minkowski 3-space

Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, and Kotaro Yamada

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Abstract

The Jorge-Meeks $n$-noid ($n\ge 2$) is a complete minimal surface of genus zero with $n$ catenoidal ends in the Euclidean 3-space $\boldsymbol{R}^3$, which has $(2\pi/n)$-rotation symmetry with respect to its axis. In this paper, we show that the corresponding maximal surface $f_n$ in Lorentz-Minkowski 3-space $\boldsymbol{R}^3_1$ has an analytic extension $\tilde f_n$ as a properly embedded zero mean curvature surface. The extension changes type into a time-like (minimal) surface.

Article information

Source
Osaka J. Math., Volume 54, Number 2 (2017), 249-272.

Dates
First available in Project Euclid: 1 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1496282423

Mathematical Reviews number (MathSciNet)
MR3657229

Zentralblatt MATH identifier
1375.53016

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53A35: Non-Euclidean differential geometry 53C50: Lorentz manifolds, manifolds with indefinite metrics

Citation

Fujimori, Shoichi; Kawakami, Yu; Kokubu, Masatoshi; Rossman, Wayne; Umehara, Masaaki; Yamada, Kotaro. Analytic extension of Jorge-Meeks type maximal surfaces in Lorentz-Minkowski 3-space. Osaka J. Math. 54 (2017), no. 2, 249--272. https://projecteuclid.org/euclid.ojm/1496282423


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References

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