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C^{2,\alpha} estimates for nonlinear elliptic equations in complex and almost complex geometry

Valentino Tosatti Northwestern University Ben Weinkove Northwestern University Yu Wang Northwestern University 杨晓奎 Morningside Center of Mathematics, AMSS, CAS

Differential Geometry mathscidoc: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.
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@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.
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