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A priori Estimates and Existence for a Class of Fully Nonlinear Elliptic Equations in Conformal Geometry*

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Abstract

In this paper we prove the interior gradient and second derivative estimates for a class of fully nonlinear elliptic equations determined by symmetric functions of eigenvalues of the Ricci or Schouten tensors. As an application we prove the existence of solutions to the equations when the manifold is locally conformally flat or the Ricci curvature is positive.

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Authors and Affiliations

  1. Centre for Mathematics and its Applications, Australian National University, Canberra ACT 0200, Australia

    Xu-Jia Wang

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  1. Xu-Jia Wang
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Correspondence to Xu-Jia Wang.

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(Dedicated to the memory of Shiing-Shen Chern)

* Project supported by the Australian Research Council.

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Wang, XJ. A priori Estimates and Existence for a Class of Fully Nonlinear Elliptic Equations in Conformal Geometry*. Chin. Ann. Math. Ser. B 27, 169–178 (2006). https://doi.org/10.1007/s11401-005-0529-6

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  • DOI: https://doi.org/10.1007/s11401-005-0529-6

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