Integration of Monge-Ampère equations and surfaces with negative gaussian curvature

• Ha Tien Ngoan ^[2] ; Dexing Kong ^[1] ; Mikio Tsuji ^[1]
  1. [1] Kyoto Sangyo University

     Kyoto Sangyo University

     Kamigyō-ku, Japón

     
  2. [2] Hanoi Institute of Mathematics, Vietnam
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 27, Nº 2, 1998, págs. 309-330
• Idioma: inglés
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• Resumen

  • We will first study the integrability condition of Monge-Ampere equations of hyperbolic type, especially of equations which describe surfaces with negative Gaussian curvature. Next, using these results, we will consider the singularities of solutions, and also of solution surfaces, of Monge-Ampere equations.

    The singularities of solutions do not generally coincide with those of solution surfaces.

    Some results of this note have been announced in [25] without proof. We will repeat some part of [25] to explain the subjects of this paper.