Existence of solutions for fully nonlinear elliptic equations on compact almost Hermitian manifolds is established under a sub-slope condition, with applications to the Hessian quotient and deformed Hermitian-Yang-Mills equations.
The twisted constant in Calabi-Yau type equation
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abstract
In this paper we establish a necessary and sufficient condition for solving a general class of fully nonlinear elliptic equations on compact almost Hermitian manifolds, extending a recent work of Guo-Song. As applications, we determine the twisted constants in Calabi-Yau type equations, including the classical one, Hessian type one and form type one with gradient terms introduced by Popovici and Tosatti-Weinkove. In particular, it addresses a question raised in a work of Chu-Tosatti-Weinkove \cite[Introduction, Remark 5]{CTW19}.
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A remark for fully non-linear elliptic equations on compact almost Hermitian manifolds
Existence of solutions for fully nonlinear elliptic equations on compact almost Hermitian manifolds is established under a sub-slope condition, with applications to the Hessian quotient and deformed Hermitian-Yang-Mills equations.