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Numerical Solutions of Boundary Value Problems for KSurfaces in R³
 NUMER. METHODS PARTIAL DIFFERENTIAL EQUATIONS
, 1996
"... A Ksurface is a surface whose Gauss curvature K is equal to a positive constant. In this paper, we will consider Ksurfaces that are defined by a nonlinear boundary value problem. In this setting, existence follows from some recent results on nonlinear secondorder elliptic partial differential equ ..."
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A Ksurface is a surface whose Gauss curvature K is equal to a positive constant. In this paper, we will consider Ksurfaces that are defined by a nonlinear boundary value problem. In this setting, existence follows from some recent results on nonlinear secondorder elliptic partial differential equations. The analytical techniques used to establish these results motivate effective numerical methods for computing Ksurfaces. In theory, the solvability of the boundary value problem reduces to the existence of a subsolution. In an analogous way, if an approximate numerical subsolution can be determined, then the corresponding Ksurface can be computed. We will consider two boundary value problems. In the first problem, the Ksurface is a graph over a plane. In the second problem, the Ksurface is a radial graph over a sphere. From certain geometrical considerations, it follows that there is a maximum allowable Gauss curvature Kmax for these problems. The principal results in this paper a...