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On a class of fully nonlinear elliptic equations containing gradient terms on compact Hermitian manifolds

  • Rirong Yuan,
    School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
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Abstract

In this paper we study a class of second order fully nonlinear elliptic equations containing gradient terms on compact Hermitian manifolds and obtain a priori estimates under proper assumptions close to optimal. The analysis developed here should be useful to deal with other Hessian equations containing gradient terms in other contexts.
Keywords: Sasakian manifold, Hermitian manifold, subsolution, extra concavity condition, fully nonlinear elliptic equation containing gradient term on complex manifold Sasakian manifold, Hermitian manifold, subsolution, extra concavity condition, fully nonlinear elliptic equation containing gradient term on complex manifold
MSC Classifications: 35J15, 53C55, 53C25, 35J25 show english descriptions Second-order elliptic equations
Hermitian and Kahlerian manifolds [See also 32Cxx]
Special Riemannian manifolds (Einstein, Sasakian, etc.)
Boundary value problems for second-order elliptic equations
35J15 - Second-order elliptic equations
53C55 - Hermitian and Kahlerian manifolds [See also 32Cxx]
53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)
35J25 - Boundary value problems for second-order elliptic equations
 

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