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
VL - 67
SP - 801
EP - 837
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
SN - 0033-5606
IS - 4
ER -