Holomorphic isometries from Poincaré disk to complex symmetric domains found.
problem Finding holomorphic isometries from the Poincaré disk to complex symmetric domains.
method Examined holomorphic isometries from the Poincaré disk into the product of the unit disk and complex unit n-ball, then extended to irreducible bounded symmetric domains of rank at least 2.
result Provided new examples of holomorphic isometries from the Poincaré disk into irreducible bounded symmetric domains of rank at least 2.
Study on holomorphic isometries between complex domains, revealing geometric properties.
problem Characterizing holomorphic isometries between bounded symmetric domains.
method Analyzing holomorphic isometries between complex unit ball and other bounded symmetric domains, using classical results for complex-analytic subvarieties of Stein manifolds.
result Images of holomorphic isometries have specific geometric properties, including intersections with affine-linear subspaces.
Study of maps between Teichmüller spaces and bounded symmetric domains.
problem Understanding isometric maps between Teichmüller spaces and bounded symmetric domains.
method Analyzing isometric maps using intrinsic Kobayashi metric from a complex analytic perspective.
result Recent results on isometric maps proved by the author.
Study characterizes totally geodesic submanifolds in quotient spaces.
problem Characterizing totally geodesic submanifolds in quotient spaces.
method Characterization through totally geodesic submanifolds and holomorphic tangent sequence splitting.
result Characterization of totally geodesic submanifolds in quotient spaces.
Uniformizes klt pairs using bounded symmetric domains.
problem Characterizing klt pairs uniformizable by bounded symmetric domains.
method Determines conditions for uniformization using Miyaoka-Yau-type inequalities.
result Characterizations of orbifold quotients of polydisc and classical bounded symmetric domains.
New metric defined for bounded symmetric domains.
problem Defining a new metric for bounded symmetric domains.
method Using generalized Hilbert metric and Borel embedding.
result The new metric differs from Carathéodory and Bergman metrics except for complex hyperbolic space.
Study reveals adversarially robust domain adaptation is harder to generalize across domains.
problem Hardness of transferring adversarial robustness across different domains.
method Analysis of adversarial Rademacher complexity over symmetric difference hypothesis space.
result Adversarial Rademacher complexity is always greater than non-adversarial, indicating intrinsic hardness.
The study examines holomorphic isometric embeddings of complex unit balls into bounded symmetric domains.
problem Holomorphic isometric embeddings of complex unit balls into bounded symmetric domains.
method Analyzes properties and structures of embeddings with non-minimal isometric constants and classifies images for specific cases.
result Complete classification of images for holomorphic isometries from (Bn,gBn) to (Ω,gΩ) for 1≤n≤n0(Ω)−1. New criterion for complex hyperbolicity of quotient spaces.
problem Understanding complex hyperbolicity in quotient spaces of bounded symmetric domains.
method Developed a new criterion for complex hyperbolicity and used it to determine subvarieties of general type.
result Quotients X with subvarieties V of dimension p ≥ 1 are of general type if a specific condition is met.
The aim of this note is to explain a generalization to the real case of a well known result on the automorphism group of an unbounded tube type symmetric domain in a complex vector space of finite dimension.
Defines twisted Blanchfield pairings for chain complexes and proves their properties.
problem Defining and analyzing twisted Blanchfield pairings for chain complexes.
method Defines twisted Blanchfield pairings for symmetric triad of chain complexes over a group ring, proving sesquilinearity, hermitian, and nonsingularity under certain conditions.
result Proves the twisted Blanchfield pairing is sesquilinear, hermitian, and nonsingular under certain conditions.
Introduces Kähler duality between domains in complex space.
problem None explicitly stated; focuses on concept introduction.
method None explicitly stated; focuses on concept introduction.
result Introduces Kähler duality between domains in complex space.
New unitary representations constructed for complex nilmanifolds.
problem Constructing unitary representations on specific geometric spaces.
method Combining geometric methods with recent developments on pseudo-Riemannian nilmanifolds.
result Developed theory for square integrable representations on complex nilmanifolds.
Study on symmetric domains with Bergman metric properties.
problem Properties of Bergman metrics in symmetric domains.
method Combining Hermitian symmetric spaces theory, Kähler immersions, and analytic/pluripotential tools.
result Rigidity results for Bergman metrics in bounded domains.
Different distances on symmetrical domains in complex space.
problem Comparing distances on specific complex domains.
method Examined Carathéodory pseudo-distance and Kähler-Einstein metric distances.
result Found the distances differ on certain complex domains.
Unified method for estimating properties of large domain distributions efficiently.
problem Estimating properties of distributions over large domains efficiently.
method Piecewise-polynomial approximation technique for constructing sample- and time-efficient estimators.
result Near-linear-time computable estimators with optimal and highly-concentrated approximation values.
Study holomorphic isometric embeddings between symmetric domains, focusing on total geodesy.
problem Holomorphic isometric embeddings between bounded symmetric domains.
method Analyzing total geodesy in reducible bounded symmetric domains with the same rank.
result Total geodesy of holomorphic isometric embeddings in reducible domains with the same rank.
Bounded symmetric domains are biholomorphic to tube domains over Finsler symmetric cones.
problem Characterizing biholomorphic mappings between tube domains and bounded symmetric domains.
method Analyzing properties of Finsler symmetric cones and unital JB-algebras.
result Tube domains over Finsler symmetric cones are biholomorphic to bounded symmetric domains.
Extends polydisk theorem to Hartogs domains over symmetric domains.
problem Rigidity phenomena in Riemannian manifolds.
method Extension of polydisk theorem to Hartogs domains over arbitrary symmetric domains.
result Dual of a Hartogs domain over a bounded symmetric domain admits no totally geodesic immersion into any compact Riemannian manifold.
In this paper we provide examples of maps from almost complex domains into pseudo-Riemannian symmetric targets, which are pluriharmonic and not integrable, i.e. do not admit an associated family. More precisely, for one class of examples the source has a non-integrable complex structure, like for instance a nearly Kaeh…
Extended contraction inequality for Rademacher complexities to vector-valued functions.
problem Bounding Rademacher complexities for vector-valued functions.
method Extended contraction inequality for Lipschitz functions with vector-valued domains, using symmetric and sub-gaussian variables.
result Rademacher variables can be replaced by arbitrary symmetric and sub-gaussian variables in the bounding expression.
Inspired by the work of G. Lu on pseudo symplectic capacities we obtain several results on the Gromov width and the Hofer--Zehnder capacity of Hermitian symmetric spaces of compact type. Our results and proofs extend those obtained by Lu for complex Grassmannians to Hermitian symmetric spaces of compact type. We also c…
It is proven a new analogue of the Theorem of Moser in a generalized context defined by Shilov Boundaries of Bounded and Symmetric Domains.
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…
The paper explores symplectic geometry of Cartan-Hartogs domains.
problem Understanding the symplectic geometry of Cartan-Hartogs domains.
method Constructing a dual counterpart and computing symplectic capacity.
result A Cartan-Hartogs domain admits symplectic duality if and only if it reduces to a complex hyperbolic space.
The study solves open problems in complex geometry by analyzing bounded domains with finite-volume quotients.
problem Analyzing bounded pseudoconvex domains with finite-volume quotients in complex geometry.
method Using semi-simplicity of automorphism groups and applying results to specific settings.
result The automorphism group of certain domains is discrete, and domains with specific properties are biholomorphic to the unit ball.
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…
Researchers describe a unique hyper-Kähler structure on a specific domain.
problem Describing a unique hyper-Kähler structure on a specific domain.
method Explicit description and computation of invariant potentials and moment maps.
result An explicit description of the unique adapted hyper-Kähler structure.
Equivalence proven between uniformizing varieties and tensors, generalizing uniformization results.
problem Characterizing complex-projective varieties with klt singularities and ample canonical divisors.
method Constructing a uniformizing variation of Hodge structure from slope zero tensors and vice versa.
result Generalization of uniformization results to singular settings, including quotients of tube domains.
New Poisson transforms link differential forms on homogeneous spaces to Riemannian symmetric spaces.
problem Linking differential forms on homogeneous spaces to Riemannian symmetric spaces.
method Construction of Poisson transforms using finite dimensional representations of reductive Lie groups.
result Explicit design of Poisson transforms compatible with BGG-complex for real hyperbolic space.
Extends Polydisk Theorem to Cartan-Hartogs domains.
problem Characterizing geodesics in Cartan-Hartogs domains.
method Applying the Polydisk Theorem to Cartan-Hartogs domains.
result Cartan-Hartogs domains inherit geodesic submanifolds from bounded symmetric domains.
This paper consists of two main results. In the first one we describe all Kaehler immersions of a bounded symmetric domain into the infinite dimensional complex projective space in terms of the Wallach set of the domain. In the second one we exhibit an example of complete and non-homogeneous Kaehler-Einstein metric wit…
No isometric holomorphic maps between Teichmüller spaces and bounded domains.
problem Holomorphic isometries between Teichmüller spaces and bounded symmetric domains.
method Analyzing intrinsic metrics and properties of Teichmüller spaces and bounded symmetric domains.
result No isometric holomorphic maps exist in dimensions two or more.
Study proves inequalities for eigenvalues of symmetric domains in space forms.
problem Eigenvalue problem for Laplacian on symmetric domains in space forms.
method Symmetry assumptions on domain, proof of inequalities for eigenvalues.
result Proves Szegö-Weinberger type inequalities for first n positive Neumann eigenvalues.
Paper proves eigenvalue inequality for Hopf-symmetric domains.
problem Eigenvalue inequality for Hopf-symmetric domains in non-compact symmetric spaces.
method Used geometric and spectral analysis on non-compact rank one symmetric spaces.
result Eigenvalue inequality for bounded Hopf-symmetric domains in non-compact symmetric spaces.
Let G/K be an irreducible Hermitian symmetric spaces of compact type with the standard homogeneous complex structure. Then the real symplectic manifold (T∗(G/K),Ω) has the natural complex structure J−. We construct all G-invariant Kähler structures (J,Ω) on homogeneous domains in T∗(G/K) anticommuting wi…
The theory of slice regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains Ω of R^4. When Ω is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which Ω is the complement of a parabola is st…
Characterizes Kähler-hyperbolicity of bounded symmetric domains based on rank and genus.
problem Understanding the Kähler-hyperbolicity of bounded symmetric domains.
method Defines Kähler-hyperbolicity length by rank and genus, and characterizes it through a special Bergman potential.
result Establishes a unique constant for Kähler-hyperbolicity based on gradient length of a Bergman potential.
Geometric proof confirms a conjecture about a metric on Cartan-Hartogs domains.
problem Proving a conjecture about a metric on Cartan-Hartogs domains.
method Computing curvature tensors to confirm the conjecture.
result The conjecture is confirmed, showing the metric's properties.
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…
New nodal domain theorems for symmetric matrices via signed graphs.
problem Establish nodal domain theorems for symmetric matrices.
method Explore signed graph structure to define nodal domains for any function.
result Improved lower bound estimates for the number of strong nodal domains.
Sharp isoperimetric inequalities for Neumann eigenvalues in symmetric spaces.
problem Finding bounds for eigenvalues of Neumann Laplacian on domains in symmetric spaces.
method Proving sharp inequalities for eigenvalues in compact and noncompact rank-1 symmetric spaces.
result Generalization of previous results for hyperbolic space and symmetric spaces.
Maps preserving Carathéodory distance between symmetric domains are rigid.
problem Rigidity of maps preserving Carathéodory distance between bounded symmetric domains.
method Large-scale geometry of Carathéodory distance, horocompactification, Gromov product.
result Maps preserving Carathéodory distance are rigid and either holomorphic or antiholomorphic.
Unified method to calculate Gromov norm for Kähler classes of bounded symmetric domains.
problem Calculating the Gromov norm of Kähler classes for all bounded symmetric domains.
method Combination of ideas from Domin-Toledo and Toledo, aided by the Polydisc Theorem.
result Unified and simplified calculation of Gromov norm for all bounded symmetric domains.
Hua domain, named after Chinese mathematician Loo-Keng Hua, is defined as a domain in Cn fibered over an irreducible bounded symmetric domain Ω⊂Cd(d<n) with the fiber over z∈Ω being a (n−d)-dimensional generalized complex ellipsoid Σ(z). In general, a Hua domain is a nonhom…
New domains of discontinuity found for Anosov representations.
problem Understanding Anosov representations acting on homogeneous spaces.
method Constructing open domains of discontinuity for Anosov representations acting on specific homogeneous spaces.
result Describes the largest possible open domains of discontinuity for Zariski dense Anosov representations.
Let E be a natural operator associated to the curvature tensor of a pseudo-Riemannian manifold. This survey article studies when the spectrum, or more generally the real Jordan normal form, of E is constant on the natural domain of definition. It deals with results for the Jacobi operator, the higher order Jacobi opera…
We construct a Weil-Petersson geodesic completion of Teichmuller space through the formalism of Coxeter complex with the Teichmuller space as its non-linear non-homogeneous fundamental domain. We show that the metric and geodesic completions both satisfy a finite rank property, demonstrating a similarity with the non-c…