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Asymptotic behavior of the sectional curvature of the Bergman metric for annuli

Włodzimierz Zwonek (2010)

Annales Polonici Mathematici

We extend and simplify results of [Din 2010] where the asymptotic behavior of the holomorphic sectional curvature of the Bergman metric in annuli is studied. Similarly to [Din 2010] the description enables us to construct an infinitely connected planar domain (in our paper it is a Zalcman type domain) for which the supremum of the holomorphic sectional curvature is two, whereas its infimum is equal to -∞ .

Asymptotic distribution and symmetric means of algebraic numbers

Igor E. Pritsker (2015)

Acta Arithmetica

Schur introduced the problem on the smallest limit point for the arithmetic means of totally positive conjugate algebraic integers. This area was developed further by Siegel, Smyth and others. We consider several generalizations of the problem that include questions on the smallest limit points of symmetric means. The key tool used in the study is the asymptotic distribution of algebraic numbers understood via the weak* limits of their counting measures. We establish interesting properties of the...

Asymptotically conformal classes and non-Strebel points

Guowu Yao (2016)

Studia Mathematica

Let T(Δ) be the universal Teichmüller space on the unit disk Δ and T₀(Δ) be the set of asymptotically conformal classes in T(Δ). Suppose that μ is a Beltrami differential on Δ with [μ] ∈ T₀(Δ). It is an interesting question whether [tμ] belongs to T₀(Δ) for general t ≠ 0, 1. In this paper, it is shown that there exists a Beltrami differential μ ∈ [0] such that [tμ] is a non-trivial non-Strebel point for any t ( - 1 / | | μ | | , 1 / | | μ | | ) 0 , 1 .

Barbilian's metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics

Wladimir G. Boskoff, Bogdan D. Suceavă (2008)

Czechoslovak Mathematical Journal

In the present paper we answer two questions raised by Barbilian in 1960. First, we study how far can the hypothesis of Barbilian's metrization procedure can be relaxed. Then, we prove that Barbilian's metrization procedure in the plane generates either Riemannian metrics or Lagrance generalized metrics not reducible to Finslerian or Langrangian metrics.

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