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A class of the non-degenerate complex quotient equations on compact Kähler manifolds

Research of the author was supported by the Natural Science Foundation of Anhui Province Education Department (grant nos. KJ2017A341 and KJ2018A0330) and the Talent Project of Fuyang Normal University (grant no. RCXM201714)
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  • In this paper, we are concerned with the equations that are in the form of the linear combinations of the elementary symmetric functions of a Hermitian matrix on compact K$ \ddot{a} $hler manifolds. Under the assumption of the cone condition, we obtain a priori estimates for the class of complex quotient equations. Then using the method of continuity, we prove an existence result.

    Mathematics Subject Classification: Primary: 35J60; Secondary: 35B45.


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