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

Jundong Zhou

doi:10.3934/cpaa.2021085

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2021, Volume 20, Issue 6: 2361-2377. Doi: 10.3934/cpaa.2021085

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

Jundong Zhou^a,b,

a.
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, China
b.
School of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, Anhui, China

Received: November 30, 2020

Revised: March 31, 2021

Early access: May 2021

Published: June 2021

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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Abstract

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.

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

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