Electron. J. Diff. Equ., Vol. 2014 (2014), No. 211, pp. 1-8.

A fully nonlinear generalized Monge-Ampere PDE on a torus

Vamsi P. Pingali

We prove an existence result for a "generalized" Monge-Ampere equation, introduced in [11], under some assumptions on a flat complex 3-torus. As an application we prove the existence of Chern connections on certain kinds of holomorphic vector bundles on complex 3-tori whose top Chern character forms are given representatives.

Submitted June 20, 2014. Published October 14, 2014.
Math Subject Classifications: 53C55.
Key Words: Monge-Ampere PDE; Chern-Weil form; Kahler manifold; Hessian equation.

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Vamsi P. Pingali
Department of Mathematics
412 Krieger Hall, Johns Hopkins University
Baltimore, MD 21218, USA
email: vpingali@math.jhu.edu

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