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arXiv · 1505.04358

A priori estimates for a generalised Monge-Ampère PDE on some compact Kähler manifolds

Vamsi Pingali
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Abstract

We study a fully nonlinear PDE involving a linear combination of symmetric polynomials of the Kähler form on a Kähler manifold. A $C^0$ \emph{a priori} estimate is proven in general and a gradient estimate is proven in certain cases. Independently, we also provide a method-of-continuity proof via a path of Kähler metrics to recover the existence of solutions in some of the known cases. Known results are then applied to an analytic problem arising from Chern-Weil theory and to a special Lagrangian-type equation arising from mirror symmetry.

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BibTeXRIS

Vamsi Pingali. 2016-01-01. A priori estimates for a generalised Monge-Ampère PDE on some compact Kähler manifolds. https://arxiv.org/abs/1505.04358

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