Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 801-837 |
| Number of pages | 37 |
| Journal | Quarterly Journal of Mathematics |
| Volume | 67 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Dec 1 2016 |
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ASJC Scopus subject areas
- Mathematics(all)
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Entire zero-mean curvature graphs of mixed type in lorentz-minkowski 3-space. / Fujimori, Shoichi; Kawakami, Yu; Kokubu, Masatoshi; Rossman, Wayne; Umehara, Masaaki; Yamada, Kotaro.
In: Quarterly Journal of Mathematics, Vol. 67, No. 4, 01.12.2016, p. 801-837.Research output: Contribution to journal › Article
}
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
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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UR - http://www.scopus.com/inward/citedby.url?scp=85041631699&partnerID=8YFLogxK
U2 - 10.1093/qmath/haw038
DO - 10.1093/qmath/haw038
M3 - Article
VL - 67
SP - 801
EP - 837
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
SN - 0033-5606
IS - 4
ER -