Bifurcation for Monge-Ampère equations on flat tori
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.
scientific article; zbMATH DE number 3852082