arXiv research

Bounded symmetric domains are biholomorphic to tube domains over Finsler symmetric cones.

Uniformizes klt pairs using bounded symmetric domains.

New metric defined for bounded symmetric domains.

In this article, we study holomorphic isometric embeddings between bounded symmetric domains. In particular, we show the total geodesy of any holomorphic isometric embedding between reducible bounded symmetric domains with the same rank.

Extends polydisk theorem to Hartogs domains over symmetric domains.

Characterizes Kähler-hyperbolicity of bounded symmetric domains based on rank and genus.

Extends Polydisk Theorem to Cartan-Hartogs domains.

Sharp isoperimetric inequalities for Neumann eigenvalues in symmetric spaces.

Study on holomorphic isometries between complex domains, revealing geometric properties.

New nodal domain theorems for symmetric matrices via signed graphs.

Unified method to calculate Gromov norm for Kähler classes of bounded symmetric domains.

Paper proves eigenvalue inequality for Hopf-symmetric domains.

This paper shows that, in dimensions two or more, there are no holomorphic isometries between Teichmüller spaces and bounded symmetric domains in their intrinsic Kobayashi metrics.

Establishes a lower bound for Kähler hyperbolicity modulus in hyperconvex domains and bounded strongly pseudoconvex domains.

We first study holomorphic isometries from the Poincaré disk into the product of the unit disk and the complex unit $n$-ball for $n\ge 2$. On the other hand, we observe that there exists a holomorphic isometry from the product of the unit disk and the complex unit $n$-ball into any irreducible bounded symmetric domain …

Study proves inequalities for eigenvalues of symmetric domains in space forms.

Maps preserving Carathéodory distance between symmetric domains are rigid.

Study proves inequality for eigenvalues in symmetric spaces.

Sharp lower bound for Hodge Laplacian on Kähler hyperbolic manifolds.

Study on symmetric domains with Bergman metric properties.

In the current article our primary objects of study are compact complex submanifolds of quotient manifolds of irreducible bounded symmetric domains by torsion free discrete lattices of automorphisms. We are interested in the characterization of the totally geodesic submanifolds among compact splitting complex submanifo…

We study general properties of holomorphic isometric embeddings of complex unit balls $\mathbb B^n$ into bounded symmetric domains of rank $\ge 2$. In the first part, we study holomorphic isometries from $(\mathbb B^n,kg_{\mathbb B^n})$ to $(Ω,g_Ω)$ with non-minimal isometric constants $k$ for any irreducible bounded s…

We prove a spanning result for vector-valued Poincaré series on a bounded symmetric domain. We associate a sequence of holomorphic automorphic forms to a submanifold of the domain. When the domain is the unit ball in ${\Bbb{C}}^n$, we provide estimates for the norms of these automorphic forms and we find asymptotics of…

An Hermitian bounded symmetric domain in a complex vector space, given in its circled realization, is endowed with two natural symplectic forms: the flat form and the hyperbolic form. In a similar way, the ambient vector space is also endowed with two natural symplectic forms: the Fubini-Study form and the flat form. I…

Study nearly geodesic immersions in symmetric spaces, leading to explicit fibrations.

Equivalence proven between uniformizing varieties and tensors, generalizing uniformization results.

We study isometric maps between Teichmüller spaces and bounded symmetric domains in their intrinsic Kobayashi metric. From a complex analytic perspective, these two important classes of geometric spaces have several features in common but also exhibit many differences. The focus here is on recent results proved by the …

Survey on bottom of spectrum of Hodge Laplacian on complete noncompact Kähler manifolds

Study proper holomorphic maps between specific domains, proving rigidity under certain conditions.

The current article stems from our study on the asymptotic behavior of holomorphic isometric embeddings of the Poincaré disk into bounded symmetric domains. As a first result we prove that any holomorphic curve exiting the boundary of a bounded symmetric domain $Ω$ must necessarily be asymptotically totally geodesic. A…

Study reveals adversarially robust domain adaptation is harder to generalize across domains.

We study proper holomorphic maps between bounded symmetric domains $D$ and $Ω$. In particular, when $D$ and $Ω$ are of the same rank $\ge 2$ such that all irreducible factors of $D$ are of rank $\ge 2$, we prove that any proper holomorphic map from $D$ to $Ω$ is a totally geodesic holomorphic isometric embedding with r…

Paper proves geodesic ball maximizes second Robin eigenvalue in non-compact symmetric spaces.

We present a new criterion for the complex hyperbolicity of a non-compact quotient X of a bounded symmetric domain. For each p $\ge$ 1, this criterion gives a precise condition under which the subvarieties V $\subset$ X with dim V $\ge$ p are of general type, and X is p-measure hyperbolic. Then, we give several applica…

Adapting the method of Andrews-Clutterbuck we prove an eigenvalue gap theorem for a class of non symmetric second order linear elliptic operators on a convex domain in euclidean space. The class of operators includes the Bakry-Emery laplacian with potential and any operator with second order term the laplacian whose fi…

In this paper we prove that given a volume, among all domains with smooth boundary in rank-1 symmetric spaces of noncompact type, geodesic balls maximizes the first nonzero Steklov eigenvalue. We also prove a comparison result for the first nonzero Steklov eigenvalue for domains in simply connected Riemannian manifolds…

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…

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…

It is proven a new analogue of the Theorem of Moser in a generalized context defined by Shilov Boundaries of Bounded and Symmetric Domains.

New method detects non-product domains using squeezing function.

We give two characterizations of varieties whose universal cover is a bounded symmetric domain without ball factors in terms of the existence of a holomorphic endomorphism \s of the tensor product T\otimes T' of the tangent bundle T with the cotangent bundle T'. To such a curvature type tensor \s one associates the fir…

We develop a theory of planar, origin-symmetric, convex domains that are inextensible with respect to lattice covering, that is, domains such that augmenting them in any way allows fewer domains to cover the same area. We show that origin-symmetric inextensible domains are exactly the origin-symmetric convex domains wi…

The paper defines Dirichlet domains for Anosov subgroups in Lie groups.

We prove that, given an acausal curve $Γ$ in the boundary at infinity of $AdS_{3}$ which is the graph of a quasi-symmetric homeomorphism $φ$, there exists a unique foliation of its domain of dependence $D(Γ)$ by constant mean curvature surfaces with bounded second fundamental form. Moreover, these surfaces provide a fa…

In this paper, we compute the derivatives of the line segment energy for a symmetric tensor field and apply them to obtain slightly more general log-concavity estimates for positive solutions of heat equations and first eigenfunctions on bounded strictly convex domains.

We consider the Johnson-Koranyi-Hua system on symmetric Siegel domains of type two. We prove that all functions which are annihilated by the system and satisfy an H^2 integrability condition are pluriharmonic. So the situation is completely different on type two domains than on tube type domains: it was proved by Johns…

We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields $\K$, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems. This class of spaces, called smooth generalized projective geometries, generaliz…

Hua domain, named after Chinese mathematician Loo-Keng Hua, is defined as a domain in $\mathbb{C}^{n}$ fibered over an irreducible bounded symmetric domain $Ω\subset \mathbb{C}^{d}\;(d<n)$ with the fiber over $z\in Ω$ being a $(n-d)$-dimensional generalized complex ellipsoid $Σ(z)$. In general, a Hua domain is a nonhom…