相关论文: Shilov boundaries determine irreducible bounded sy…

We show that there are many sets in the boundary of a bounded symmetric domain that determine the values and norm of holomorphic functions on the domain having continuous extensions to the boundary. We provide an analogue of the…

We prove that a proper holomorphic map between two bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the…

In this note, an isoperimetric inequality for the harmonic mean of lower order Steklov eigenvalues is proved on bounded domains in noncompact rank-$1$ symmetric spaces. This work extends result of \cite{BR.01} and \cite{V.21} proved for…

We prove a number of results on the automorphisms of and isomorphisms between Hardy-Toeplitz algebras $\mathcal{T}(D)$ associated to bounded symmetric domains $D$: that the stable isomorphism class of $\mathcal{T}(D)$ determines $D$ (even…

We prove that, under some generic non-degeneracy assumptions, real analytic, centrally symmetric plane domains are determined by their Dirichlet (resp. Neumann) spectra. We prove that the conditions are open-dense for real analytic convex…

Let M be an irreducible Riemannian symmetric space. The index of M is the minimal codimension of a (non-trivial) totally geodesic submanifold of M. We prove that the index is bounded from below by the rank of the symmetric space. We also…

Let ${\cal D}$ be a bounded symmetric domain of tube type, $S$ its Shilov boundary, and $G$ the neutral component of its group of biholomorphic transforms. We classify the orbits of $G$ in the set $S\times S\times S$.

We show that the first order Sobolev spaces on cuspidal symmetric domains can be characterized via pointwise inequalities. In particular, they coincide with the Hajlasz-Sobolev spaces.

We introduce the concept of orthogonal structure on complex Grassmannians. Based on this structure, we define the notion of orthogonal mappings. This class of maps generalizes holomorphic maps between the Shilov boundaries of type-I bounded…

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

A form of Sobolev inequalities for the symmetric gradient of vector-valued functions is proposed, which allows for arbitrary ground domains in $\mathbb R ^n$. In the relevant inequalities, boundary regularity of domains is replaced with…

The article contains the results of the author's recent investigations of rigidity problems of domains in Euclidean spaces carried out for developing a new approach to the classical problem of the unique determination of bounded closed…

We prove that the irreducible symmetric space of complex structures on $\mathbb R^{2n}$ (resp.\ quaternionic structures on $\mathbb C^{2n}$) is spectrally unique within a $2$-parameter (resp.\ $3$-parameter) family of homogeneous metrics on…

We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.

Our goal is to establish what seems to be the first rigidity result for CR embeddings between Shilov boundaries of bounded symmetric domains of higher rank. The result states that any such CR embedding is the standard linear embedding up to…

In this paper we study the geometry and the topology of unbounded domains in the Hyperbolic Space $\mathbb{H} ^n$ supporting a bounded positive solution to an overdetermined elliptic problem. Under suitable conditions on the elliptic…

We prove that two proper holomorphic polynomial maps between bounded symmetric domains of classical type which preserve the origin are equivalent if and only if they are isotropically equivalent.

Motivated by the classical bounded H\"{o}lder domains, we introduce the notion of an unbounded simply connected H\"{o}lder domain. We prove analytic and geometric characterizations of those domains with the aid of the spherical metric and…

We extend the concept of a finite dimensional {\it holomorphic homogeneous regular} (HHR) domain and some of its properties to the infinite dimensional setting. In particular, we show that infinite dimensional HHR domains are domains of…