Tohoku Mathematical Journal
2026
September
SECOND SERIES VOL. 78, NO. 3

Tohoku Math. J.
78 (2026), 443-466

Title SEPARABLE ZERO MEAN CURVATURE SURFACES IN MINKOWSKI 3-SPACE

Author Daehwan Kim and Yuta Ogata

(Received January 16, 2025, revised February 27, 2025)
Abstract. Zero mean curvature (ZMC) surfaces in Minkowski 3-space are surfaces that have zero mean curvature, which may contain spacelike, timelike or mixed-type parts. In this paper, we will consider a setup without conformal coordinates, i.e. implicit equations for ZMC surfaces, which can produce ZMC surfaces with any causalities. We classify all solutions to the equation for ZMC surfaces with the separable form. Consequently, we obtain many new examples of not only triply, doubly or singly periodic ZMC surfaces, but also entire ZMC-graphs.

Mathematics Subject Classification. Primary 53B30; Secondary 53C42.
Key words and phrases. Zero mean curvature surface, elliptic function, separable surface, periodicity, entire graph.

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