Bifurcation for Monge-Ampère equations on flat tori
type: Item
instance of: scholarly article
title: Bifurcation for Monge-Ampère equations on flat tori
zbMATH Open document ID: 0536.58034
DOI: 10.1007/BF01168578
published in: Manuscripta Mathematica
publication date: 1983-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/154972
review text: The author investigates the bifurcation phenomenon for elliptic solutions of the equation \(\frac{\det(g+\nabla^ 2\phi)}{\det g}=\exp(-\lambda \phi)\), where g is a Riemannian metric on a manifold V and \(\nabla^ 2\phi\) the matrix of second covariant derivatives. Using standard methods he studies in detail the problem in the case where V is torus with the usual flat metric.
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 35J15
zbMATH DE Number: 3852082
zbMATH Keywords: elliptic solutions
zbMATH Keywords: second covariant derivatives
author: Philippe P. Delanoë
reviewed by: Vladimir I. Oliker
MaRDI profile type: Publication
cites work: Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
cites work: Equations du type Monge-Ampère sur les variétés Riemanniennes compactes. I
cites work: Equations du type de Monge-Ampère sur les variétés Riemanniennes compactes. II
cites work: Group theoretic methods in bifurcation theory. With an appendix by P. Olver
cites work: Q4141653
OpenAlex ID: W2157579315
description: scientific article; zbMATH DE number 3852082