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arXiv · 1402.0554

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

Valentino Tosatti·Yu Wang·Ben Weinkove·Xiaokui Yang
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Abstract

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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Valentino Tosatti, Yu Wang, Ben Weinkove, Xiaokui Yang. 2014-02-04. $C^{2,\alpha}$ estimates for nonlinear elliptic equations in complex and almost complex geometry. https://doi.org/10.1007/s00526-014-0791-0

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