$C^{2,\alpha}$ estimates for nonlinear elliptic equations in complex and almost complex geometry
Differential Geometry
2015-09-01 v2 Analysis of PDEs
Complex Variables
Abstract
We describe how to use the perturbation theory of Caffarelli to prove Evans-Krylov type estimates for solutions of nonlinear elliptic equations in complex geometry, assuming a bound on the Laplacian of the solution. Our results can be used to replace the various Evans-Krylov type arguments in the complex geometry literature with a sharper and more unified approach. In addition, our methods extend to almost-complex manifolds, and we use this to obtain a new local estimate for an equation of Donaldson.
Cite
@article{arxiv.1402.0554,
title = {$C^{2,\alpha}$ estimates for nonlinear elliptic equations in complex and almost complex geometry},
author = {Valentino Tosatti and Yu Wang and Ben Weinkove and Xiaokui Yang},
journal= {arXiv preprint arXiv:1402.0554},
year = {2015}
}
Comments
26 pages, v2 final version, to appear in Calc. Var. PDE