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

Ben Weinkove; Valentino Tosatti; Xiaokui Yang; Yu Wang

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C^(2,α) estimates for nonlinear elliptic equations in complex and almost complex geometry

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arxiv 1402.0554 v2 pith:L6LBX6TP submitted 2014-02-04 math.DG math.APmath.CV

C^(2,α) estimates for nonlinear elliptic equations in complex and almost complex geometry

Valentino Tosatti , Yu Wang , Ben Weinkove , Xiaokui Yang This is my paper

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keywords complexgeometryalphaellipticequationsestimatesevans-krylovnonlinear

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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.

C^(2,α) estimates for nonlinear elliptic equations in complex and almost complex geometry

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