Related papers: Boundary points, minimal $L^2$ integrals and conca…

We develop new techniques to compute the weighted $L^2$-cohomology of quasi-fibered boundary metrics (QFB-metrics). Combined with the decay of $L^2$-harmonic forms obtained in a companion paper, this allows us to compute the reduced…

Our interest is a regularity of a minimal singular metric of a line bundle. One main conclusion of our general result in this paper is the existence of continuous Hermitian metrics with semi-positive curvatures on the so-called Zariski's…

A-manifolds and A-bundles are manifolds and vector bundles modelled on a projective finitely generated module over a topological algebra A. In this paper we investigate the conditions under which an A-bundle is provided with an A-valued…

We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…

This paper investigates the cohomological property of vector bundles on biprojective space. We will give a criterion for a vector bundle to be isomorphic to the tensor product of pullbacks of exterior products of differential sheaves.

Let $H$ be a real Hilbert space. In this short note, using some of the properties of bounded linear operators with closed range defined on $H$, certain bounds for a specific convex subset of the solution set of infinite linear…

After a review of the general properties of holomorphic spheres in complex surfaces we describe the local geometry in the vicinity of a CP^1 embedded with a negative normal bundle. As a by-product, we build (asymptotically locally…

We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $E\rightarrow M$, over a Riemannian manifold $M$, when $E$ is endowed with a…

Wavelet frames for $L^2({\mathbb R})$ can be characterized by means of spectral techniques. This work uses spectral formulas to determine all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed finite number of generators of…

Let $X$ be a compact complex manifold of dimension $n$ and let $m$ be a positive integer with $m\leq n$. Assume that $X$ admits a K\"ahler metric $\omega$ and a weakly positive, $\partial\bar\partial$-closed, smooth $(n-m,\,n-m)$-form…

We study the moduli space of parabolic connections of rank two on the complex projective line $\mathbb{P}^1$ minus five points with fixed spectral data. This paper aims to compute the cohomology of the structure sheaf and a certain vector…

Let $X$ be a Hyperk\"ahler manifold, and let $H$ be an ample divisor on $X$. We give a lower bound in terms of the Beauville-Bogomolov form $q(H)$ for the twisted cotangent bundle $\Omega_X \otimes H$ to be pseudoeffective. If $X$ is…

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 a few splitting criteria for vector bundles on a quadric hypersurface and Grassmannians. We give also some cohomological splitting conditions for rank 2 bundles on multiprojective spaces. The tools are monads and a Beilinson's type…

The purpose of this note is twofold. First we show that, for weakly differentiable maps between Riemannian manifolds of any dimension, a smallness condition on a Morrey-norm of the gradient is sufficient to guarantee that the pulled-back…

This paper addresses the topological structures induced on vector spaces by convex modulars that do not satisfy the $\Delta_2$ condition, with particular focus on their applications to variable exponent spaces such as \( \ell^{(p_n)} \) and…

In this paper, we study classes of discrete convex functions: submodular functions on modular semilattices and L-convex functions on oriented modular graphs. They were introduced by the author in complexity classification of minimum…

In these (not-completed) notes, we study the Hartogs extension phenomenon for holomorphic sections of holomorphic vector bundles over complex analytic varieties. Namely, we study properties of the Hartogs extension phenomenon with respect…

We study moduli of holomorphic vector bundles on non-compact varieties. We discuss filtrability and algebraicity of bundles and calculate dimensions of local moduli. As particularly interesting examples, we describe numerical invariants of…

We use Dirac operator techniques to a establish sharp lower bound for the first eigenvalue of the Dolbeault Laplacian twisted by Hermitian-Einstein connections on vector bundles of negative degree over compact K\"ahler manifolds.