Isometric Immersions of Surfaces with Two Classes of Metrics and Negative Gauss Curvature
نویسندگان
چکیده
The isometric immersion of two-dimensional Riemannian manifolds or surfaces with negative Gauss curvature into the three-dimensional Euclidean space is studied in this paper. The global weak solutions to the Gauss-Codazzi equations with large data in L∞ are obtained through the vanishing viscosity method and the compensated compactness framework. The L∞ uniform estimate and H−1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type. The global weak solutions in L∞ to the Gauss-Codazzi equations yield the C isometric immersions of surfaces with the given metrics.
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