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Bifurcation for Monge-Ampère equations on flat tori. (English) Zbl 0536.58034

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.
Reviewer: V.Oliker

MSC:

58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
35B32 Bifurcations in context of PDEs
53C20 Global Riemannian geometry, including pinching
35J15 Second-order elliptic equations
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References:

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