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Dirichlet problem for Krylov type equation in conformal geometry

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Abstract

In this paper, we study a class of nonlinear elliptic equations in the Krylov type, which can be viewed as a generalization of the Hessian equation for Schouten tensor. After a conformal change, we considered the Dirichlet problem for a modified Schouten tensor in the smooth closed Riemannian manifold with smooth boundary. A unique k-admissible solution can be assured under some suitable settings.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310058, China

    **nying Liu & Weimin Sheng

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  1. **nying Liu
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  2. Weimin Sheng
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Correspondence to Weimin Sheng.

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Communicated by L. Szekelyhidi.

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The authors were supported by NSFC, Grant Nos. 11971424 and 12031017.

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Liu, X., Sheng, W. Dirichlet problem for Krylov type equation in conformal geometry. Calc. Var. 63, 59 (2024). https://doi.org/10.1007/s00526-024-02665-0

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