Related papers: A general extension theorem for cohomology classes…

We prove an Ohsawa-Takegoshi-type extension theorem on the Berkovich closed unit disc over a complete non-Archimedean field. As an application, we establish a non-Archimedean analogue of Demailly's regularization theorem for…

We establish a new extension result for twisted canonical forms defined on a hypersurface with simple normal crossings of a projective manifold. Some of the examples presented in the appendix are showing that the bounds we obtain for the…

Let $(X,J,\omega,g)$ be a complete $n$-dimensional K\"ahler manifold. A Theorem by Gromov \cite{G} states that the if the K\"ahler form is $d$-bounded, then the space of harmonic $L_2$ forms of degree $k$ is trivial, unless $k=\frac{n}{2}$.…

In this note, making use of noncommutative $l$-adic cohomology, we extend the generalized Riemann hypothesis from the realm of algebraic geometry to the broad setting of geometric noncommutative schemes in the sense of Orlov. As a first…

Based on a recent extension theorem for reflexive differential forms, that is, regular differential forms defined on the smooth locus of a possibly singular variety, we study the geometry and cohomology of sheaves of reflexive…

We obtain a general Ohsawa-Takegoshi extension theorem by using the Ross-Witt Nystr\"om correspondence picture and Berndtsson's theorem in \cite{Bern20}. In the test configuration ($\mathbb C^*$-degeneration) case, our approach gives a…

In the present paper we study abelian extensions of connected Lie groups $G$ modeled on locally convex spaces by smooth $G$-modules $A$. We parametrize the extension classes by a suitable cohomology group $H^2_s(G,A)$ defined by locally…

The aim of this work is to generalize the ultraholomorphic extension theorems from V. Thilliez in the weight sequence setting and from the authors in the weight function setting (of Roumieu type) to a mixed framework. Such mixed results…

Employing Morse theory for the global control of monodromy and the method of analytic discs for local extension, we establish a version of the global Hartogs extension theorem in a singular setting: for every domain D of an (n-1)-complete…

In $L^2$ extension theorems from a singular hypersurface in a complex manifold, important roles are played by certain measures such as the Ohsawa measure which determine when a given function can be extended. We show that the singularity of…

In these notes we generalize the Ohsawa's results on the Hartogs extension phenomenon in the complement of effective divisors in K\"ahler manifolds with semipositive non-flat normal bundle. Namely, we prove that the Hartogs extension…

In an influential $L^2$ extension theorem due to Demailly, the finiteness of an $L^2$ norm called the Ohsawa norm determines whether a given holomorphic function can be extended. This result has been further generalized by Zhou and Zhu to…

Let $X=U/K$ be a compact Hermitian symmetric space, and let $\sE$ be a $U$-homogeneous Hermitian vector bundle on $X$. In a previous paper, we showed that the space of nearly holomorphic sections is well-adapted for harmonic analysis in…

We prove an $L^2$-$\partial\overline\partial$-Lemma involving smooth square integrable forms on complete K\"ahler manifolds, provided that the unique self-adjoint extension of the Hodge Laplacian on the Hilbert space of $L^2$-forms has a…

We study the following optimal $L^2$ extension problem of openness type: given a complex manifold $M$, a closed subvariety $S\subset M$ and a holomorphic vector bundle $E\rightarrow M$, for any $L^2$ holomorphic section $f$ defined on some…

Hosono obtained sharper estimates of the Ohsawa--Takegoshi $L^2$-extention theorem by allowing the constant depending on the weight function for a domain in $\mathbb{C}$. In this article, we show the higher dimensional case of sharper…

In this article we prove a theorem of Ohsawa-Takegoshi type on compact K\"ahler manifolds. Our arguments follow the "standard" approach for this kind of extension results; however, there are many complications arising from the…

We study conditions of H\"ormander's $L^2$-estimate and the Ohsawa-Takegoshi extension theorem. Introducing a twisted version of H\"ormander-type condition, we show a converse of H\"ormander $L^2$-estimate under some regularity assumptions…

We prove an extension theorem for roots and logarithms of holomorphic line bundles across strictly pseudoconcave boundaries: they extend in all cases except one, when dimension and Morse index of a critical point is two. In that case we…

In very rough terms, the main theorem is that the set, which consists of semistable vector bundles with trivial rational Chern classes and nontrivial kth cohomology on a smooth complex projective variety, is a degeneration of a union of…