@article{ASNSP_1998_4_27_2_309_0,
author = {Ha Tien Ngoan and Kong, Dexing and Tsuji, Mikio},
title = {Integration of {Monge-Amp\`ere} equations and surfaces with negative gaussian curvature},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {309--330},
year = {1998},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 27},
number = {2},
mrnumber = {1664691},
zbl = {0978.53006},
language = {en},
url = {https://www.numdam.org/item/ASNSP_1998_4_27_2_309_0/}
}
TY - JOUR AU - Ha Tien Ngoan AU - Kong, Dexing AU - Tsuji, Mikio TI - Integration of Monge-Ampère equations and surfaces with negative gaussian curvature JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1998 SP - 309 EP - 330 VL - 27 IS - 2 PB - Scuola normale superiore UR - https://www.numdam.org/item/ASNSP_1998_4_27_2_309_0/ LA - en ID - ASNSP_1998_4_27_2_309_0 ER -
%0 Journal Article %A Ha Tien Ngoan %A Kong, Dexing %A Tsuji, Mikio %T Integration of Monge-Ampère equations and surfaces with negative gaussian curvature %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1998 %P 309-330 %V 27 %N 2 %I Scuola normale superiore %U https://www.numdam.org/item/ASNSP_1998_4_27_2_309_0/ %G en %F ASNSP_1998_4_27_2_309_0
Ha Tien Ngoan; Kong, Dexing; Tsuji, Mikio. Integration of Monge-Ampère equations and surfaces with negative gaussian curvature. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 27 (1998) no. 2, pp. 309-330. https://www.numdam.org/item/ASNSP_1998_4_27_2_309_0/
[ 1 ] , Des surfaces à courbure constante négative dans l'espace à trois dimensions et de leurs singularités, Math. Ann. 130 (1955), 234-256. | Zbl | MR
[2] - , "Methods of Mathematical Physics", vol. 2, Interscience, New York, 1962. | Zbl
[3] , "Leçons sur la théorie générale des surfaces", tome3, Gauthier-Villars, Paris, 1894.
[4] , Generation of singularities on surfaces of negative curvature, Maht. USSR-Sb. 64 (1964), 286-320. | Zbl | MR
[5] , "Leçons sur l'intégration des équations aux dérivées partielles du second ordre", tome 1, Hermann, Paris, 1896.
[6] , "Cours d'analyse mathématique", tome 3, Gauthier-Villars, Paris, 1927. | JFM
[7] , "Le problème de Cauchy et les équations aux dérivées partielles linéaires hyperboliques", Hermann, Paris, 1932. | Zbl | JFM
[8] , Über Flächen von constanter Gausscher Krümmung, Trans. Amer. Math. Soc. 2 (1901), 87-99. | MR | JFM
[9] , Sur les surfaces à courbure constante négative, C. R. Acad. Sci. Paris 134 (1902), 740-743. | JFM
[10] , Geometric singularities for Hamilton-Jacobi equation, Adv. Stud. Pure Math. 22 (1993), 89-100. | Zbl | MR
[11] , Characteristic vector fields for first order partial differential equations, preprint. | MR
[12] - , Semi-local classification of geometric singularities for Hamilton-Jacobi equations, J. Differential Equations 118 (1995), 166-193. | Zbl | MR
[13] , Local existence of multivalued solutions to analytic symplectic Monge-Ampère equations, Indiana Univ. Math. J. 40 (1991), 123-148. | Zbl | MR
[14] , Über das Anfangswertproblem einer hyperbolischen nichtlinearen partiellen Differentialgleichung zveiler Ordnung mit zwei unabhänggigen Veränderlichen, Math. Ann. 97 (1927), 179-191. | JFM
[15] , A priori limitations for solutions of Monge-Ampère equations I, II, Trans. Amer. Math. Soc. 37 (1934), 417-434; 41 (1937), 365-374. | MR | JFM
[16] , Contact geometry and non-linear second order differential equations, Russian Math. Surveys 34 (1979), 149-180. | Zbl | MR
[17] , Efimov's theorem about complete immersed surfaces of negative curvature, Adv. Math. 8 (1972), 454-543. | Zbl | MR
[18] , Formation of singularities for Hamilton-Jacobi equations in several space variables, J. Math. Soc. Japan 43 (1991), 89-100. | Zbl | MR
[19] , Formation of shocks for a single conservation law, SIAM J. Math. Anal. 19 (1988), 1391-1408. | Zbl | MR
[20] , Characteristics of nonlinear partial differential equations, Bull. Polish Acad. Sci. Math, Cl.III2 (1954), 419-422. | Zbl | MR
[21] , On surfaces with negative analytic Gaussian curvature, Diploma at Hanoi Institute of Mathematics (1996).
[22] , Formation of singularities for Hamilton-Jacobi equations II, J. Math. Kyoto Univ. 26 (1986), 299-308. | Zbl | MR
[23] , Prolongation of classical solutions and singularities of generelized solutions, Ann. Inst. H. Poincaré - Anal. Non Linéaire 7 (1990), 505-525. | Zbl | MR | Numdam
[24] , Formation of singularities for Monge-Ampère equations, Bull. Sci. Math. 119 (1995), 433-457. | Zbl | MR
[25] , Monge-Ampère equations and surfaces with negative Gaussian curvature, Banach Center Publ. 39 (1997), 161-170. | Zbl | MR
[26] , Geometric approach to blow-up phenomena in nonlinear problems, In "Real Analytic and Algebraic Singularities" edited by T. Fukuda, et al. (Pitman Research Notes in Math. 381. Longman, 1998), 164-180. | Zbl | MR
[27] , On singularities of mappings of Euclidean spaces I, Ann. Math. 62 (1955), 374-410. | Zbl | MR





