相关论文: Intrinsic metrics in polygonal domains
We study planar domains $G$ equipped with a hyperbolic type metric and approximate geodesics that join two points $x,y \in G$ and their lengths. We present an algorithm that enables one to approximate the shortest distance in polygonal…
We establish geometric relationships between the average scale-invariant Cassinian metric and other hyperbolic type metrics. In addition, we study the local convexity properties of the scale-invariant metric balls in Euclidean once…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints…
We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal prediction. Distances between "infinitesimally close"…
This paper generalizes D. Burago and S. Ivanov's work on filling volume minimality and boundary rigidity of almost real hyperbolic metrics. We show that regions with metrics close to a negatively curved symmetric metric are strict minimal…
We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function…
The purpose of this article is to investigate the boundary behaviour of the Kobayashi--Fuks metric and several associated invariants on strictly pseudoconvex domains in the paradigm of scaling. This approach allows us to examine more…
We introduce two valuation-based deviations on convex bodies. Using a construction that allows us to associate to these deviations "intrinsic" pseudometrics, we establish various results which capture information about the underlying…
We study the boundary regularity of proper holomorphic mappings between strictly pseudoconvex domains with $C^2$-boundaries.
We discuss an alternative approach to the uniformisation problem on surfaces with boundary by representing conformal structures on surfaces $M$ of general type by hyperbolic metrics with boundary curves of constant positive geodesic…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
We study on the biholomorphic equivalence of a strongly pseudoconvex bounded domain with differentiable spherical boundary to an open ball, and we study on the biholomorphicity of a proper holomorphic self mapping of a strongly pseudoconvex…
A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most \pi. We can thus talk about the convexity of a set of points in terms of the…
Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…
In this article we continue the study of properties of squeezing functions and geometry of bounded domains. The limit of squeezing functions of a sequence of bounded domains is studied. We give comparisons of intrinsic positive forms and…
We explore the Steklov eigenvalue problem on convex polygons, focusing mainly on the inverse Steklov problem. Our primary finding reveals that, for almost all convex polygonal domains, there exist at most finitely many non-congruent domains…
We prove some results concerning the boundary of a convex set in $\H^n$. This includes the convergence of curvature measures under Hausdorff convergence of the sets, the study of normal points, and, for convex surfaces, a generalized Gauss…
We study holomorphic isometries between bounded symmetric domains with respect to the Bergman metrics up to a normalizing constant. In particular, we first consider a holomorphic isometry from the complex unit ball into an irreducible…