Surface in \(R^ 3\) with prescribed Gauss curvature
The author proves that for every smooth function K(x,y) which vanishes on a simple closed smooth curve \(\Lambda\) and which satisfies \(dK|_{\Lambda}\neq 0\) there always exists a smooth surface \(z=z(x,y)\) defined in a neighbourhood of \(\Lambda\) with Gaussian curvature K(x,y).
scientific article; zbMATH DE number 4036611