Mini-Workshop Complex Analysis and applications, 27-28. februar 2012.

• 24. Фебруар, 2012
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Mini-Workshop "Complex Analysis and applications" одржаће се у понедељак 27. и уторак 28. фебруара 2012. на Математичком факултету у сали БИМ, IV спрат.

Распоред излагања:

Понедељак, 27. фебруар, 12 часова, сала БИМ

1. Matti Vuorinen, University of Turku, Finland

"Quasihyperbolic geometry and quasiconformal maps"

Abstract: This talk is a survey of my recent work with my coauthors during the past year. The talk is divided into four parts, each part based on a preprint. X. Zhang and G. Wang are PhD students at the University of Turku.

M. Vuorinen and G. Wang: Bisection of geodesic segments in hyperbolic geometry. arXiv:1108.2948v2 [math. MG]

2. Миодраг Матељевић, Владимир Божин, Миљан Кнежевић, Математички факултет, Универзитет у Београду

"Quasiconformality of harmonic mappings between smooth Jordan domains"

Abstract: Suppose that $h$ is a harmonic mapping of the unit disc onto a $displaystyle C^{1,,alpha}$ domain $D$. Then $h$ is q.c. if and only if it is bi-Lipschitz. In particular, we consider sufficient and necessary conditions in terms of boundary function that $h$ is q.c. We give a review of recent related results including the case if domain is the upper half plane. We also consider harmonic mapping with respect to $ ho$ metric on codomain.

3. Давид Калај, Природноматематички факултет, Универзитет Црне Горе

"Deformations of Annuli on Riemann surfaces and the generalization of Nitsche conjecture"

4. Дискусија



Уторак, 28. фебруар, 11 часова, сала БИМ

1. Stamatis Pouliasis, Aristotle University, Thessaloniki, Greece

"Versions of Schwarz`s lemma for condenser capacity and inner radius"

Abstract: We will consider variants of the classical Schwarz`s lemma involving  monotonicity properties of condenser capacity and inner radius. Also, we will examine when a similar monotonicity property holds for the hyperbolic metric. This is joint work with D. Betsakos.

2. Iason Efraimidis, Aristotle University, Thessaloniki, Greece

"Variations of Schwarz lemma"

Abstract: Suppose that f maps the unit disc D holomorphically into D and f(0)=0. A classical inequality due to Littlewood generalizes Schwarz’s lemma and asserts that every w in f(D) has modulus less or equal to the product of the modulus of its pre-images. We present a similar inequality proved by D.Betsakos, in which the assumption of f(D) being a subset of D is replaced by the weaker assumption Diamf(D)=2. The main tools in the proof are Green’s function and Steiner symmetrization.

 3. Весна Манојловић, Факултет организационих наука, Универзитет у Београду

"Boundary modulus of continuity and quasiconformal mappings"

Abstract: Let $D$ be a bounded domain in $mathbb R^n$, $n geq 2$, and let $f$ be a continuous mapping of $overline D$ into $mathbb R^n$ which is quasiconformal in $D$. Suppose that $|f(x) - f(y)| leq omega(|x-y|)$ for all $x$ and $y$ in $partial D$, where $omega$ is a non-negative non-decreasing function satisfying $omega(2t) leq 2omega(t)$ for $t geq 0$. We prove, with an additional growth condition on $omega$, that $|f(x) - f(y)| leq C max {omega(|x-y|), |x-y|^alpha }$ for all $x, y in D$, where $alpha =K_I(f)^{1/(1-n)}$. The talk is based on [AMN].

[AMN] Miloš Arsenović, Vesna Manojlović and Raimo Nakki

"Boundary modulus of continuity and quasiconformal mappings, to appear in Ann. Acad. Sci. Fenn."

4. Миша Арсеновић, Математички факултет, Универзитет у Београду
(наслов и абстракт излагања ће бити накнадно објављени)

5. Дискусија