[Surfaces de courbure moyenne nulle dans
Il est bien connu que les surfaces maximales de type espace et les surfaces minimales de type temps dans lʼespace
It is well known that space-like maximal surfaces and time-like minimal surfaces in Lorentz–Minkowski 3-space
Accepté le :
Publié le :
S. Fujimori 1 ; Y.W. Kim 2 ; S.-E. Koh 3 ; W. Rossman 4 ; H. Shin 5 ; H. Takahashi 6 ; M. Umehara 7 ; K. Yamada 8 ; S.-D. Yang 2
@article{CRMATH_2012__350_21-22_975_0, author = {S. Fujimori and Y.W. Kim and S.-E. Koh and W. Rossman and H. Shin and H. Takahashi and M. Umehara and K. Yamada and S.-D. Yang}, title = {Zero mean curvature surfaces in $ {\mathbf{L}}^{3}$ containing a light-like line}, journal = {Comptes Rendus. Math\'ematique}, pages = {975--978}, publisher = {Elsevier}, volume = {350}, number = {21-22}, year = {2012}, doi = {10.1016/j.crma.2012.10.024}, language = {en}, }
TY - JOUR AU - S. Fujimori AU - Y.W. Kim AU - S.-E. Koh AU - W. Rossman AU - H. Shin AU - H. Takahashi AU - M. Umehara AU - K. Yamada AU - S.-D. Yang TI - Zero mean curvature surfaces in $ {\mathbf{L}}^{3}$ containing a light-like line JO - Comptes Rendus. Mathématique PY - 2012 SP - 975 EP - 978 VL - 350 IS - 21-22 PB - Elsevier DO - 10.1016/j.crma.2012.10.024 LA - en ID - CRMATH_2012__350_21-22_975_0 ER -
%0 Journal Article %A S. Fujimori %A Y.W. Kim %A S.-E. Koh %A W. Rossman %A H. Shin %A H. Takahashi %A M. Umehara %A K. Yamada %A S.-D. Yang %T Zero mean curvature surfaces in $ {\mathbf{L}}^{3}$ containing a light-like line %J Comptes Rendus. Mathématique %D 2012 %P 975-978 %V 350 %N 21-22 %I Elsevier %R 10.1016/j.crma.2012.10.024 %G en %F CRMATH_2012__350_21-22_975_0
S. Fujimori; Y.W. Kim; S.-E. Koh; W. Rossman; H. Shin; H. Takahashi; M. Umehara; K. Yamada; S.-D. Yang. Zero mean curvature surfaces in $ {\mathbf{L}}^{3}$ containing a light-like line. Comptes Rendus. Mathématique, Volume 350 (2012) no. 21-22, pp. 975-978. doi : 10.1016/j.crma.2012.10.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.10.024/
[1] Generalized maximal surfaces in Lorentz–Minkowski space
[2] S. Fujimori, Y.W. Kim, S.-E. Koh, W. Rossman, H.‘Shin, M. Umehara, K. Yamada, S.-D. Yang, Zero mean curvature surfaces in Lorentz–Minkowski 3-space which change type across a light-like line, preprint.
[3] New maximal surfaces in Minkowski 3-space with arbitrary genus and their cousins in de Sitter 3-space, Results Math., Volume 56 (2009), pp. 41-82
[4] The extremal surfaces in the 3-dimensional Minkowski space, Acta Math. Sinica, Volume 1 (1985), pp. 173-180
[5] Timelike minimal surfaces via loop groups, Acta Appl. Math., Volume 83 (2004), pp. 313-335
[6] A family of maximal surfaces in Lorentz–Minkowski three-space, Proc. Amer. Math. Soc., Volume 134 (2006), pp. 3379-3390
[7] Prescribing singularities of maximal surfaces via a singular Björling representation formula, J. Geom. Phys., Volume 57 (2007), pp. 2167-2177
[8] Spacelike maximal surfaces, timelike minimal surfaces, and Björling representation formulae, J. Korean Math. Soc., Volume 48 (2011), pp. 1083-1100
[9] Zero mean curvature surfaces of mixed type in Minkowski space, Izv. Math., Volume 67 (2003), pp. 209-224
[10] Maximal surfaces in the 3-dimensional Minkowski space
[11] Maximal surfaces with singularities in Minkowski space, Hokkaido Math. J., Volume 35 (2006), pp. 13-40
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- Classification of zero mean curvature surfaces of separable type in Lorentz-Minkowski space, Tohoku Mathematical Journal, Volume 74 (2022) no. 2 | DOI:10.2748/tmj.20210120a
- Reflection principle for lightlike line segments on maximal surfaces, Annals of Global Analysis and Geometry, Volume 59 (2021) no. 1, p. 93 | DOI:10.1007/s10455-020-09743-4
- Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds, Advances in Mathematics, Volume 365 (2020), p. 107036 | DOI:10.1016/j.aim.2020.107036
- Improvement of the Bernstein-type theorem for space-like zero mean curvature graphs in Lorentz-Minkowski space using fluid mechanical duality, Proceedings of the American Mathematical Society, Series B, Volume 7 (2020) no. 2, p. 17 | DOI:10.1090/bproc/44
- Wick rotations of solutions to the minimal surface equation, the zero mean curvature equation and the Born–Infeld equation, Proceedings - Mathematical Sciences, Volume 129 (2019) no. 3 | DOI:10.1007/s12044-019-0479-7
- Space-like maximal surfaces containing entire null lines in Lorentz-Minkowski 3-space, Proceedings of the Japan Academy, Series A, Mathematical Sciences, Volume 95 (2019) no. 9 | DOI:10.3792/pjaa.95.97
- Hypersurfaces with Light-Like Points in a Lorentzian Manifold, The Journal of Geometric Analysis, Volume 29 (2019) no. 4, p. 3405 | DOI:10.1007/s12220-018-00118-7
- Retraction Note to: Extremal surface with the light-like line in Minkowski space
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, Boundary Value Problems, Volume 2018 (2018) no. 1 | DOI:10.1186/s13661-018-0994-y - Quadrics and Scherk towers, Monatshefte für Mathematik, Volume 186 (2018) no. 2, p. 249 | DOI:10.1007/s00605-017-1075-5
- RETRACTED ARTICLE: Extremal surface with the light-like line in Minkowski space
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, Boundary Value Problems, Volume 2017 (2017) no. 1 | DOI:10.1186/s13661-017-0786-9 - CAUSAL CHARACTERS OF ZERO MEAN CURVATURE SURFACES OF RIEMANN TYPE IN THE LORENTZ-MINKOWSKI 3-SPACE, Kyushu Journal of Mathematics, Volume 71 (2017) no. 2, p. 211 | DOI:10.2206/kyushujm.71.211
- Surfaces With Light-Like Points In Lorentz-Minkowski 3-Space With Applications, Lorentzian Geometry and Related Topics, Volume 211 (2017), p. 253 | DOI:10.1007/978-3-319-66290-9_14
- Global weak and smooth solutions of the equation for timelike extremal surface in Minkowski space, Journal of Mathematical Analysis and Applications, Volume 428 (2015) no. 2, p. 1135 | DOI:10.1016/j.jmaa.2015.02.088
- Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space, Michigan Mathematical Journal, Volume 63 (2014) no. 1 | DOI:10.1307/mmj/1395234364
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