Related papers: A solution of an $L^{2}$ extension problem with op…

We prove an $L^2$ extension theorem of Ohsawa-Takegoshi type for extending holomorphic sections of line bundles from a subvariety which is given as a maximal log-canonical center of a pair and is of general codimension in a projective…

In a recent result by the authors (ref. [1]) it was proved that solutions of the self-similar fragmentation equation converge to equilibrium exponentially fast. This was done by showing a spectral gap in weighted $L^2$ spaces of the…

Carleson showed that the Bergman space for a domain on the plane is trivial if and only if its complement is polar. Here we give a quantitative version of this result. One is the Suita conjecture, established by the first-named author in…

The goal of this contribution is to investigate L${}^2$ extension properties for holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi…

We generalize the inequality being a counterpart of the several complex variables version of the Suita conjecture. For this aim higher order generalizations of the Bergman kernel are introduced. As a corollary some new partial results on…

We find a precise relationship between the minimal extensions in $L^2$ and $L^p$ Ohsawa-Takegoshi extension theorems. This relationship also gives another proof to the $L^p$ version of the Ohsawa-Takegoshi extension theorem, which is…

Using various results from extremal set theory (interpreted in the language of additive combinatorics), we prove an asyptotically sharp version of Freiman's theorem in F_2^n: if A in F_2^n is a set for which |A + A| <= K|A| then A is…

In this paper, I prove a very general extension theorem for log pluricanonical systems. The main application of this extension theorem is (together with Kawamata's subadjunction theorem) to give an optimal subadjunction theorem which…

We study the extension estimates for paraboloids in d-dimensional vector spaces over finite fields F_q with q elements. We use the connection between L^2 based restriction estimates and L^p\to L^r extension estimates for paraboloids. As a…

We prove the optimal $L^2$-extension theorem of Ohsawa-Takegoshi type on a tube domain. As an application, we give a simple proof of Pr\'ekopa's theorem.

We prove extensions of the estimates of Aleksandrov and Bakel$'$man for linear elliptic operators in Euclidean space $\Bbb{R}^{\it n}$ to inhomogeneous terms in $L^q$ spaces for $q < n$. Our estimates depend on restrictions on the…

In this paper we give a short, elementary proof of the following too extreme cases of the Leopoldt conjecture: the case when $\K/\Q$ is a solvable extension and the case when it is a totally real extension in which $p$ splits completely.…

We prove an extension theorem for effective plt pairs $(X,S+B)$ of non-negative Kodaira dimension $\kappa (K_X+S+B)\geq 0$. The main new ingredient is a refinement of the Ohsawa-Takegoshi $L^2$ extension theorem involving singular hermitian…

The purpose of this note is to show that the di-bar-estimate which is needed in the Ohsawa-Takegoshi Extension Theorem [6] is a direct consequence of the Hormander-Kohn-Morrey weigthed inequality. In this inequality, the Donnelly-Fefferman…

We establish an expansion theory for $\text{SL}_2(\mathbb Z/q\mathbb Z)$. Incorporating this into a framework recently developed by Shkredov, we confirm Zaremba's conjecture.

In this paper, we prove the boundedness of the Bergman projection on weighted mixed norm spaces of the upper-half space for some weights that are constructed using the logarithm function and growth functions. Our necessary and sufficient…

We use the principle of almost orthogonality to give a new and simple proof that a sparse Lerner operator is bounded on a matrix- or operator-weighted space $L_W^{2}(\mu)$, where $\mu$ is a doubling measure on $\R^d$ if and only if the…

We utilize the Legendre-Fenchel transform and weak geodesics for plurisubharmonic functions to construct a weight function that can be used in the Berndtsson-Lempert method, to give an Ohsawa-Takegoshi extension type of result. Theorem 4.1…

In this article, we present characterizations of the concavity property of minimal $L^2$ integrals degenerating to linearity in the case of fibrations over open Riemann surfaces. As applications, we obtain characterizations of the holding…

Let $E \subseteq \mathbb{R}^n$ be a union of line segments and $F \subseteq \mathbb{R}^n$ the set obtained from $E$ by extending each line segment in $E$ to a full line. Keleti's line segment extension conjecture posits that the Hausdorff…