TY - JOUR

T1 - Entire zero-mean curvature graphs of mixed type in lorentz-minkowski 3-space

AU - Fujimori, Shoichi

AU - Kawakami, Yu

AU - Kokubu, Masatoshi

AU - Rossman, Wayne

AU - Umehara, Masaaki

AU - Yamada, Kotaro

N1 - Funding Information:
Fujimori was partially supported by the Grant-in-Aid for Young Scientists (B) No. 25800047, Kawakami was supported by the Grant-in-Aid for Scientific Research (C) No. 15K04845, Rossman by Grant-in-Aid for Scientific Research (C) No. 15K04845, Umehara by (A) No. 26247005 and Yamada by (C) No. 26400066 from Japan Society for the Promotion of Science.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - It is classically known that the only entire zero-mean curvature graphs in the Euclidean 3-space are planes, by Bernstein's theorem. A surface in Lorentz-Minkowski 3-space R3 1is called of mixed type if it changes causal type from space-like to time-like. In R3 1 Osamu Kobayashi found two entire zero-mean curvature graphs of mixed type that are not planes. As far as the authors know, these two examples were the only known examples of entire zero-mean curvature graphs of mixed type without singularities. In this paper, we construct several families of real analytic entire zero-mean curvature graphs of mixed type in Lorentz-Minkowski 3-space. The entire graphs mentioned above lie in one of these classes.

AB - It is classically known that the only entire zero-mean curvature graphs in the Euclidean 3-space are planes, by Bernstein's theorem. A surface in Lorentz-Minkowski 3-space R3 1is called of mixed type if it changes causal type from space-like to time-like. In R3 1 Osamu Kobayashi found two entire zero-mean curvature graphs of mixed type that are not planes. As far as the authors know, these two examples were the only known examples of entire zero-mean curvature graphs of mixed type without singularities. In this paper, we construct several families of real analytic entire zero-mean curvature graphs of mixed type in Lorentz-Minkowski 3-space. The entire graphs mentioned above lie in one of these classes.

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U2 - 10.1093/qmath/haw038

DO - 10.1093/qmath/haw038

M3 - Article

AN - SCOPUS:85041631699

SN - 0033-5606

VL - 67

SP - 801

EP - 837

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 4

ER -