Monge-Ampère equations and surfaces with negative Gaussian curvature

Volume 39 / 1997

Mikio Tsuji Banach Center Publications 39 (1997), 161-170 DOI: 10.4064/-39-1-161-170


In [24], we studied the singularities of solutions of Monge-Ampère equations of hyperbolic type. Then we saw that the singularities of solutions do not coincide with the singularities of solution surfaces. In this note we first study the singularities of solution surfaces. Next, as the applications, we consider the singularities of surfaces with negative Gaussian curvature. Our problems are as follows: 1) What kinds of singularities may appear?, and 2) How can we extend the surfaces beyond the singularities?


  • Mikio Tsuji

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