Geometric methods for solving Codazzi and Monge-Ampère equations
type: Item
instance of: scholarly article
title: Geometric methods for solving Codazzi and Monge-Ampère equations
zbMATH Open document ID: 0934.53029
DOI: 10.1007/BF01459727
author: Ulrich Pinkall
author: Angela Schwenk-Schellschmidt
author: Udo Simon
published in: Mathematische Annalen
publication date: 2000-04-10T00:00:00Z
full work available at URL: https://eudml.org/doc/165163
review text: 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.
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 537309
zbMATH Keywords: Codazzi equation
zbMATH Keywords: projective structure
zbMATH Keywords: conformal structure
zbMATH Keywords: Minkowski problem
zbMATH Keywords: ovaloid
MaRDI profile type: Publication
Wikidata QID: Q125073663
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OpenAlex ID: W2086427009
description: scientific article; zbMATH DE number 537309