# MathSciDoc: An Archive for Mathematician ∫

#### Differential Geometrymathscidoc:1610.10005

Cal. Var. PDE, 53, 431-453, 2015
We describe how to use the perturbation theory of Caffarelli to prove Evans-Krylov type $C^{2,\alpha}$ 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.
@inproceedings{valentino2015c^{2,\alpha},
title={C^{2,\alpha} estimates for nonlinear elliptic equations in complex and almost complex geometry},
author={Valentino Tosatti, Ben Weinkove, Yu Wang, and 杨晓奎},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161003224902598650063},
booktitle={Cal. Var. PDE},
volume={53},
pages={431-453},
year={2015},
}

Valentino Tosatti, Ben Weinkove, Yu Wang, and 杨晓奎. C^{2,\alpha} estimates for nonlinear elliptic equations in complex and almost complex geometry. 2015. Vol. 53. In Cal. Var. PDE. pp.431-453. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161003224902598650063.