Related papers: Geometry of homogeneous polynomials in ${\mathbb R…
In this paper we characterize the extremal points of the unit ball of the Benamou--Brenier energy and of a coercive generalization of it, both subjected to the homogeneous continuity equation constraint. We prove that extremal points…
The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix…
We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph $H$ to $n$-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new…
We prove a bound for the geodesic diameter of a subset of the unit ball in $\mathbb{R}^n$ described by a fixed number of quadratic equations and inequalities, which is polynomial in $n$, whereas the known bound for general degree is…
In this paper, we investigate some properties of pluriharmonic mappings defined in the unit ball. First, we discuss some geometric univalence criteria on pluriharmonic mappings, and then establish a Landau-Bloch theorem for a class of…
Orthogonal polynomials with respect to the hypergeometric distribution on lattices in polyhedral domains in ${\mathbb R}^d$, which include hexagons in ${\mathbb R}^2$ and truncated tetrahedrons in ${\mathbb R}^3$, are defined and studied.…
In this paper, we study the structure of homogeneous subgroups of the homeomorphism group of the sphere, which are defined as closed groups of homeomorphisms of the sphere that contain the rotation group. We prove two structure theorems…
We first give an exposition on holomorphic isometries from the Poincar\'e disk to polydisks and from the Poincar\'e disk to the product of the Poincar\'e disk with a complex unit ball. As an application, we provide an example of proper…
The polynomial cluster value problem replaces the role of the continuous linear functionals in the original cluster value problem for the continuous polynomials to describe the corresponding cluster sets and fibers. We prove several…
We study lower bounds for the norm of the product of polynomials and their applications to the so called \emph{plank problem.} We are particularly interested in polynomials on finite dimensional Banach spaces, in which case our results…
The numerical range of holomorphic mappings arises in many aspects of nonlinear analysis, finite and infinite dimensional holomorphy, and complex dynamical systems. In particular, this notion plays a crucial role in establishing exponential…
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…
The resultant veriety in the space of systems of homogeneous polynomials of given degrees consists of such systems having non-trivial solutions. We calculate the integer cohomology groups of all spaces of non-resultant systems of…
We present a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes a mass uniformly distributed on the sphere. First, connection formulas relating these multivariate orthogonal…
The problem of covering a region of the plane with a fixed number of minimum-radius identical balls is studied in the present work. An explicit construction of bi-Lipschitz mappings is provided to model small perturbations of the union of…
In this paper we define the magnitude of metric spaces using measures rather than finite subsets as had been done previously and show that this agrees with earlier work with Leinster in arXiv:0908.1582. An explicit formula for the magnitude…
We define bounded cohomology of $t$-discrete measured groupoids with coefficients into measurable bundles of Banach spaces. Our approach via homological algebra extends the classic theory developed by Ivanov and by Monod. As a consequence,…
We study the group of surjective linear isometries on certain real Banach sequence spaces using the preservation of extreme points in the closed unit ball. Our main result provides a characterization of the extreme points of the dual unit…
The compact set of homogeneous quadratic polynomials in $n$ real variables with modulus bounded by 1 on the unit sphere $S^{n-1}$ is trivially semi-definite representable. The compact set of homogeneous ternary quartics with modulus bounded…
We observe that a large part of the volume of a hyperbolic polyhedron is taken by a tubular neighbourhood of its boundary, and use this to give a new proof for the finiteness of arithmetic maximal reflection groups following a recent work…