Osaka Journal of Mathematics

Zero mean curvature surfaces in Lorentz--Minkowski 3-space which change type across a light-like line

S. Fujimori, Y.W. Kim, S.-E. Koh, W. Rossman, H. Shin, M. Umehara, K. Yamada, and S.-D. Yang

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Abstract

It is well-known that space-like maximal surfaces and time-like minimal surfaces in Lorentz--Minkowski $3$-space $\boldsymbol{R}^{3}_{1}$ have singularities in general. They are both characterized as zero mean curvature surfaces. We are interested in the case where the singular set consists of a light-like line, since this case has not been analyzed before. As a continuation of a previous work by the authors, we give the first example of a family of such surfaces which change type across a light-like line. As a corollary, we also obtain a family of zero mean curvature hypersurfaces in $\boldsymbol{R}^{n+1}_{1}$ that change type across an ($n-1$)-dimensional light-like plane.

Article information

Source
Osaka J. Math., Volume 52, Number 1 (2015), 285-299.

Dates
First available in Project Euclid: 24 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1427202882

Mathematical Reviews number (MathSciNet)
MR3326612

Zentralblatt MATH identifier
1319.53008

Subjects
Primary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
Secondary: 53B30: Lorentz metrics, indefinite metrics 35M10: Equations of mixed type

Citation

Fujimori, S.; Kim, Y.W.; Koh, S.-E.; Rossman, W.; Shin, H.; Umehara, M.; Yamada, K.; Yang, S.-D. Zero mean curvature surfaces in Lorentz--Minkowski 3-space which change type across a light-like line. Osaka J. Math. 52 (2015), no. 1, 285--299. https://projecteuclid.org/euclid.ojm/1427202882


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References

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