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Title

Monge-Ampère equations and surfaces with negative Gaussian curvature

Authors 1

Affiliations

  1. Department of Mathematics, Kyoto Sangyo University Kamigamo, Kita-ku, Kyoto 603, Japan

Abstract

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?

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Banach Center Publications
1997/39/1
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Pages:
161-170
Main language of publication
English
Published
1997
Exact and natural sciences