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A Note on Pluriharmonic Functions in the Unit Polydisc in ℂn
We prove Schwarz-Pick lemma for bounded and strictly positive pluriharmonic functions in the unit polydisc in ℂ n . We give a distance estimate in...
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Boundary Regularity of Isometries Between Infinitely Flat Complex Domains
In this paper we prove that isometries with respect to the Kobayashi metric between certain domains having boundary points at which the boundary is...
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A Vanishing Theorem on a Class of Hartogs Domain
In this paper, we consider the d -boundedness of the Bergman metric and a vanishing theorem of L 2 -cohomology on a class of Hartogs domain, whose base...
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Weighted boundary limits of the Kobayashi--Fuks metric on h-extendible domains
We study the boundary behavior of the Kobayashi--Fuks metric on the class of h-extendible domains. Here, we derive the nontangential boundary...
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On Fridman Invariants and Generalized Squeezing Functions
In this paper, the authors introduce the notion of generalized squeezing function and study the basic properties of generalized squeezing functions...
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Complex Geodesics in Tube Domains and Their Role in the Study of Harmonic Map**s in the Disc
We continue the research on the structure of complex geodesics in tube domains over (bounded) convex bases. In some special cases a more explicit...
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Geometry of holomorphic invariant strongly pseudoconvex complex Finsler metrics on the classical domains
In this paper, a class of holomorphic invariant metrics is introduced on the irreducible classical domains of types I–IV, which are strongly...
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Analytic Interpolation into the Tetrablock and a μ-synthesis Problem
We give a solvability criterion for a special case of the μ-synthesis problem. That is, we prove the necessity and sufficiency of a condition for the...
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The Schwarz Lemma at the Boundary of the Non-Convex Complex Ellipsoids
Let B 2, p := { z ∈ ℂ 2 : ∣ z 1 ∣ 2 + ∣ z 2 ∣ p < 1} (0 < p < 1). Then, B 2, p (0 < p < 1) is a non-convex complex ellipsoid in ℂ 2 without smooth boundary. In this...
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Parametrix for the localization of the Bergman metric on strictly pseudoconvex domains
We give the parameter version of a localization theorem for the Bergman metric near the boundary points of strictly pseudoconvex domains. The...
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Carathéodory extremal functions on the symmetrized bidisc
We show how realization theory can be used to find the solutions of the Carathéodory extremal problem on the symmetrized bidisc...
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Canonical metrics on generalized Cartan-Hartogs domains
In this paper, the author considers a class of bounded pseudoconvex domains, i.e., the generalized Cartan-Hartogs domains Ω( μ , m ). The first result...
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On behaviour of holomorphically contractible systems under non-monotonic sequences of sets
The new results concerning the continuity of holomorphically contractible systems treated as set functions with respect to non-monotonic sequences of...
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Geometry and Arithmetic on the Siegel–Jacobi Space
The Siegel–Jacobi space is a non–symmetric homogeneous space which is very important geometrically and arithmetically. In this paper, we discuss the...
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k-metric spaces
In this paper, we give a new generalization of metric spaces called k -metric spaces. Our k -metrics are valued in lattice ordered groups, which allows...
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Some Analysable Instances of μ-synthesis
I describe a verifiable criterion for the solvability of the 2×2 spectral Nevanlinna-Pick problem with two interpolation points, and likewise for...