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arXiv · 1509.05853

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

Shoichi Fujimori·Yu Kawakami·Masatoshi Kokubu·Wayne Rossman·Masaaki Umehara·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.

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Shoichi Fujimori, Yu Kawakami, Masatoshi Kokubu, Wayne Rossman, Masaaki Umehara, Kotaro Yamada. 2015-09-19. Analytic extension of Jorge-Meeks type maximal surfaces in Lorentz-Minkowski 3-space. https://arxiv.org/abs/1509.05853

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