A priori estimates for a generalised Monge-Amp\`ere PDE on some compact K\"ahler manifolds
Differential Geometry
2016-01-05 v2 Mathematical Physics
Complex Variables
math.MP
Abstract
We study a fully nonlinear PDE involving a linear combination of symmetric polynomials of the K\"ahler form on a K\"ahler manifold. A \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 K\"ahler 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.
Keywords
Cite
@article{arxiv.1505.04358,
title = {A priori estimates for a generalised Monge-Amp\`ere PDE on some compact K\"ahler manifolds},
author = {Vamsi Pingali},
journal= {arXiv preprint arXiv:1505.04358},
year = {2016}
}
Comments
Final version. To appear in Complex Variables and Elliptic Equations