Geometric methods for solving Codazzi and Monge-Ampère equations
In [\textit{U. Simon}, Bull. Soc. Math. Belg. 45, 25-34 (1993; Zbl 0804.53036)], we studied the uniqueness problem for certain Monge-Ampère equations on a compact, simply connected, projectively flat manifold \(M\). We now solve the corresponding existence problem by a systematic study of Codazzi-relations between projective and conformal structures in Sects. 1-3. In Sect. 4 we apply this to the given existence problem for certain Monge-Ampère operators on manifolds diffeomorphic to the unit sphere \(S^n\). As an application we present another affine version of the Euclidean Minkowski problem for ovaloids in Sect. 5.
scientific article; zbMATH DE number 537309