ﻻ يوجد ملخص باللغة العربية
Let $(X,omega)$ be a compact Kahler manifold of dimension $n$ and fix $1leq mleq n$. We prove that the total mass of the complex Hessian measure of $omega$-$m$-subharmonic functions is non-decreasing with respect to the singularity type. We then solve complex Hessian equations with prescribed singularity, and prove a Hodge index type inequality for positive currents.
Given a complex manifold $X$, any Kahler class defines an affine bundle over $X$, and any Kahler form in the given class defines a totally real embedding of $X$ into this affine bundle. We formulate conditions under which the affine bundles arising t
Let $(X,omega)$ be a compact K{a}hler manifold with a K{a}hler form $omega$ of complex dimension $n$, and $Vsubset X$ is a compact complex submanifold of positive dimension $k<n$. Suppose that $V$ can be embedded in $X$ as a zero section of a holomor
In this paper, we consider Hessian equations with its structure as a combination of elementary symmetric functions on closed Kahler manifolds. We provide a sufficient and necessary condition for the solvability of these equations, which generalize th
In the present paper, we show that given a compact Kahler manifold $(X,omega)$ with a Kahler metric $omega$, and a complex submanifold $Vsubset X$ of positive dimension, if $V$ has a holomorphic retraction structure in $X$, then any quasi-plurisubhar
Let $Omega Subset mathbb C^n$ be a bounded strongly $m$-pseudoconvex domain ($1leq mleq n$) and $mu$ a positive Borel measure on $Omega$. We study the complex Hessian equation $(dd^c u)^m wedge beta^{n - m} = mu$ on $Omega$. First we give a suffi