Related papers: Koll\'ar's injectivity theorem for globally $F$-re…

We treat a relative version of the main theorem in my previous paper: A transcendental approach to Koll\'ar's injectivity theorem. More explicitly, we give a curvature condition that implies Koll\'ar type cohomology injectivity theorems in…

We prove an analytic generalization of Koll\'ar's vanishing theorem, which contains the Nadel vanishing theorem as a special case.

We note that the vanishing and injectivity theorems of Koll\'ar and Esnault-Viehweg can be used to give a quick algebraic proof of a strengthening of the Ein-Lazarsfeld Skoda-type division theorem for global sections of adjoint line bundles…

In this paper we study the question asked by Caucher Birkar about injectivity theorem on cohomologies of generalised pairs. By applying techniques from complex analytic geometry, we show that the injectivity theorem holds for generalised…

We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.

We prove a generalized Fej\'er's theorem for locally compact groups.

We generalize the injectivity theorem of Esnault and Viehweg, and apply it to the structure of log canonical type divisors.

We generalize Koll\'ar's conjecture (including torsion freeness, injectivity theorem, vanishing theorem and decomposition theorem) to Saito's $S$-sheaves twisted by a $\mathbb{Q}$-divisor. This gives a uniform treatment for various kinds of…

Let $G$ be some generalized $\pi$-soluble groups and ${\cal F}$ be a Fitting set of $G$. In this paper, we prove the existence and conjugacy of ${\cal F}$-injectors of $G$, and give a description of the structure of the injectors.

Let $f:X\rightarrow Y$ be a smooth fibration between two complex manifolds $X$ and $Y$, and let $L$ be a pseudo-effective line bundle on $X$. We obtain a sufficient condition for $R^{q}f_{\ast}(K_{X/Y}\otimes L)$ to be reflexive and hence…

One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems and present a couple of applications of them.

In this article we study certain specialization properties of the index of varieties defined by Koll\'{a}r.

We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the…

Let $F: \mathbb{R}^n\to\mathbb{R}^n$ be a $C^{\infty}$ map such that $DF(x)$ is invertible for every $x\in\mathbb{R}^n$. Although being a local diffeomorphism, $F$ is not necessarily globally injective if $n\geq2$. Finding additional…

We extend the injectivity theorem of Esnault and Viehweg to a class of non-normal log varieties, which contains normal crossings log varieties, and is closed under the operation of taking the $\LCS$ locus.

We prove a strengthening of Koll\'ar's Ampleness Lemma and use it to prove that any proper coarse moduli space of stable log-varieties of general type is projective. We also prove subadditivity of log-Kodaira dimension for fiber spaces…

We establish a Liouville type theorem for some conformally invariant fully nonlinear equations

We prove the generalized Wolff's Ideal Theorem on certain uniformly closed subalgebras of $ H^{\infty}(\mathbb{D}) $ on which the Corona Theorem is already known to hold.

We find Feynman-Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measure-valued coefficients.

We prove some injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology groups with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional…