arXiv research

Extends Polydisk Theorem to Cartan-Hartogs domains.

Extends polydisk theorem to Hartogs domains over symmetric domains.

The paper explores symplectic geometry of Cartan-Hartogs domains.

The Cartan-Hartogs domains are defined as a class of Hartogs type domains over irreducible bounded symmetric domains. For a Cartan-Hartogs domain $Ω^{B}(μ)$ endowed with the natural Kähler metric $g(μ),$ Zedda conjectured that the coefficient $a_2$ of the Rawnsley's $\varepsilon$-function expansion for the Cartan-Harto…

We prove the existence of a Berezin-Engliš quantization for Cartan-Hartogs domains.

The Fock-Bargmann-Hartogs domain $D_{n,m}(μ)$ ($μ>0$) in $\mathbf{C}^{n+m}$ is defined by the inequality $\|w\|^2<e^{-μ\|z\|^2},$ where $(z,w)\in \mathbf{C}^n\times \mathbf{C}^m$, which is an unbounded non-hyperbolic domain in $\mathbf{C}^{n+m}$. Recently, Yamamori gave an explicit formula for the Bergman kernel of the…

The Cartan-Hartogs domains are defined as a class of Hartogs type domains over irreducible bounded symmetric domains. The purpose of this paper is twofold. Firstly, for a Cartan-Hartogs domain $Ω^{B^{d_0}}(μ)$ endowed with the canonical metric $g(μ)$, we obtain an explicit formula for the Bergman kernel of the weighted…

Study Bergman metric on Cartan-Hartogs domains and their duals.

Inspired by the work of Z. Lu and G. Tian [21] in the compact setting, in this paper we address the problem of studying the Szegö kernel of the disk bundle over a noncompact Kähler manifold. In particular we compute the Szegö kernel of the disk bundle over a Cartan-Hartogs domain based on a bounded symmetric domain. Th…

Rigidity theorem for Bergman metric on Hartogs domains over bounded homogeneous domains.

We extend a result of Z. Feng and Z. Tu by showing that if one of the coefficients $a_j$, $2\leq j\leq n$, of Rawnlsey's epsilon function associated to a $n$-dimensional Cartan-Hartogs domain is constant, then the domain is biholomorphically equivalent to the complex hyperbolic space.

An $n$-dimensional Hartogs domain $D_F$ with strongly pseudoconvex boundary can be equipped with a natural \K metric $g_F$. In this paper we prove that if $g_F$ is an extremal \K metric then $(D_F, g_F)$ is biholomorphically isometric to the $n$-dimensional complex hyperbolic space.

The Fock-Bargmann-Hartogs domain $D_{n,m}$ in $\mathbb{C}^{n+m}$ is defined by the inequality $\|w\|^2<e^{-\|z\|^2},$ where $(z,w)\in \mathbb{C}^n\times \mathbb{C}^m$, which is an unbounded non-hyperbolic domain in $\mathbb{C}^{n+m}$. This paper mainly consists of three parts. Firstly, we give the explicit expression o…

In this paper we address two problems concerning a family of domains $M_Ω(μ) \subset \C^n$, called Cartan-Hartogs domains, endowed with a natural Kaehler metric $g(μ)$. The first one is determining when the metric $g(μ)$ is extremal (in the sense of Calabi), while the second one studies when the coefficient $a_2$ in th…

An n-dimensional strictly pseudoconvex Hartogs domain D_F can be equipped with a natural Kaehler metric g_F. In this paper we prove that if m_0g_F is balanced for a given positive integer m_0 then m_0>n and (D_F, g_F) is holomorphically isometric to an open subset of the n-dimensional complex hyperbolic space.

100 years ago exactly, in 1906, Hartogs published a celebrated extension phenomenon (birth of Several Complex Variables), whose global counterpart was stated in full generality later by Osgood (1929): holomorphic functions in a connected neighborhood V(bD) of a connected boundary bD contained in C^n (n >= 2) do extend …

This paper consists of two results dealing with balanced metrics (in S. Donaldson terminology) on nonconpact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only Cartan-Hartogs domain which admits a balanced metric is the complex hyperbolic spac…

An $n$-dimensional Hartogs domain $D_F$ with strongly pseudoconvex boundary can be equipped with a natural Kaehler metric $g_F$. This paper contains two results. In the first one we prove that if $g_F$ is an extremal Kaehler metric then $(D_F, g_F)$ is holomorphically isometric to an open subset of the $n$-dimensional …

The Fock-Bargmann-Hartogs domain $D_{n,m}(μ)$ ($μ>0$) in $\mathbb{C}^{n+m}$ is defined by the inequality $\|w\|^2<e^{-μ\|z\|^2},$ where $(z,w)\in \mathbb{C}^n\times \mathbb{C}^m$, which is an unbounded non-hyperbolic domain in $\mathbb{C}^{n+m}$. This paper introduces a Kähler metric $αg(μ;ν)$ $(α>0)$ on $D_{n,m}(μ)$, …

The definition of balanced metrics was originally given by Donaldson in the case of a compact polarized Kähler manifold in 2001, who also established the existence of such metrics on any compact projective Kähler manifold with constant scalar curvature. Currently, the only noncompact manifolds on which balanced metrics…

Let $D_F = \{(z_0, z) \in {\C}^{n} | |z_0|^2 < b, \|z\|^2 < F(|z_0|^2) \}$ be a strongly pseudoconvex Hartogs domain endowed with the \K metric $g_F$ associated to the \K form $ω_F = -\frac{i}{2} \partial \bar{\partial} \log (F(|z_0|^2) - \|z\|^2)$. This paper contains several results on the Riemannian geometry of thes…

In this paper we study Kaehler manifolds that are strongly not relative to any projective Kaehler manifold, i.e. those Kaehler manifolds that do not share a Kaehler submanifold with any projective Kaehler manifold even when their metric is rescaled by the multiplication by a positive constant. We prove two results whic…

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 normal complex space X of pure dimension n >= 2 and for every compact set K in D …

Vanishing result for cohomology leads to extension theorem for pluriharmonic functions.

Every holomorphic effective parabolic or reductive geometry on a domain over a Stein manifold extends uniquely to the envelope of holomorphy of the domain. This result completes the open problems of my earlier paper on extension of holomorphic geometric structures on complex manifolds. We use this result to classify th…

Study on when Bergman metrics of domains are induced by balls.

In this paper, we solve in the negative the following problem : Is there any complex structure on the sphere S^6?

Paper extends Ohsawa-Takegoshi theorem to more general domains, proving removable singularities for plurisubharmonic functions.

We prove that a real-valued function (that is not assumed to be continuous) on a real analytic manifold is analytic whenever all its restrictions to analytic submanifolds homeomorphic to the 2-sphere are analytic. This is a real analog for the classical theorem of Hartogs that a function on a complex manifold is comple…

This is the first of a series of papers, in which we study the plurigenera, the Kodaira dimension and more generally the Iitaka dimension on compact almost complex manifolds. Based on the Hodge theory on almost complex manifolds, we introduce the plurigenera, Kodaira dimension and Iitaka dimension on compact almost com…

Method generates intermediate domains to align source and target domains.

Aims to eliminate domain bias in authentication without domain labels.

CoDAG combines domain adaptation and generalization for unsupervised continual domain shift learning.

DCASE 2022 Task 2 tackles domain shifts in ASD for machine condition monitoring.

Adaptive multi-domain learning reduces parameter count for efficient deep learning.

Recently multi-domain recommender systems have received much attention from researchers because they can solve cold-start problem as well as support for cross-selling. However, when applying into multi-domain items, although algorithms specifically addressing a single domain have many difficulties in capturing the spec…

Proposes novel losses for fine-grained categorical domain adaptation.

Improves unsupervised domain adaptation by mixing source and target domains.

We address the problem of domain generalization where a decision function is learned from the data of several related domains, and the goal is to apply it on an unseen domain successfully. It is assumed that there is plenty of labeled data available in source domains (also called as training domain), but no labeled dat…

MetFA aligns source and target domains for cross-device image classification.

In this paper, we propose a simple model referred as Contradistinguisher (CTDR) for unsupervised domain adaptation whose objective is to jointly learn to contradistinguish on unlabeled target domain in a fully unsupervised manner along with prior knowledge acquired by supervised learning on an entirely different domain…

CSD learns a common component for domain generalization, outperforming existing methods.

Method learns domain-specific representations without supervision.

A new method uses normalizing flows for gradual domain adaptation.

We propose a method to infer domain-specific models such as classifiers for unseen domains, from which no data are given in the training phase, without domain semantic descriptors. When training and test distributions are different, standard supervised learning methods perform poorly. Zero-shot domain adaptation attemp…

Study shows how many domains are needed for generalization, using a new measure called domain shattering dimension.

TAROT enhances robustness and domain adaptability with domain-invariant features.

A new model for imputing missing values in time series data across domains.