Lipšicov prostor i kvazikonformna preslikavanja

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Lipšicov prostor i kvazikonformna preslikavanja

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dc.contributor.advisor Mateljević, Miodrag
dc.contributor.author Ababoub, Ali
dc.date.accessioned 2013-10-08T09:31:39Z
dc.date.available 2013-10-08T09:31:39Z
dc.date.issued 2013
dc.identifier.uri http://hdl.handle.net/123456789/3048
dc.description.abstract This thesis has been written under the supervision of my mentor Prof. Miodrag Mateljevi c, and my co-mentor dr. Vladimir Bo zin at the University of Belgrade in the academic year 2012-2013. The topic of this thesis is Complex analysis related with geometric function theory, more precisely the theory of quasiconformal mappings in the Euclidean n-dimensional space. For good survey of the eld, see F. W. Gehring [20] in the handbook of K uhnau [33] which also contains many other surveys on quasiconformal mappings and related topics. The main source in this dissertation is J. V ais al a [67]. The thesis is divided into three chapters. Chapter 1 is divided into 5 sections. In this chapter, we focus on quasiconformal mappings in Rn and discuss various equivalent de nitions. We give The Modulus of family of curves in the rst section, geometric de nition of quasiconformal space mappings in second section, analytic de nition of quasiconformal space mappings in third section, equivalence of the de nitions in fourth section, and the Beltrami equation in fth section. Chapter 2 is divided into 5 sections. We begin by generalizing the class of Lip ( ), 0 < 1, and some properties of that class. Chapter 2 is devoted to understanding the properties by introducing the notion of Linearity, Di erentiability, and majorants. A majorant function is a certain generalization of the power functions t , this is done in the rst section. In the second section we introducing the notion of moduli of continuity with its Some Properties which gotten from I.M. Kolodiy, F. Hildebrand paper [39]. In third section we produced harmonic mapping as preliminary for the fourth section which including subharmonicity of jfjq of harmonic quasiregular mapping in space. In the last section we introducing estimation of the Poisson kernel which were extracted from Krantz paper [42]. Chapter 3 is divided into 3 sections. This chapter is include the main result in this dissertation. In this chapter we prove that !u( ) C!f ( ), where u : ! Rn is the harmonic extension of a continuous map f : @ ! Rn, if u is a K-quasiregular map and is bounded in Rn with C2 boundary. Here C is a constant depending only on n, !f and K and !h denotes the modulus of continuity of h. We also prove a version of this result for !-extension domains with c-uniformly perfect boundary and quasiconformal mappings, and we state some results regarding HQC self maps of the quadrant Q = fz : z = x + iy; x; y > 0g. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2013-10-08T09:31:38Z No. of bitstreams: 1 Ali Ababaoub Lipschitz Space and Quasicionformal Mappings.pdf: 501408 bytes, checksum: ba59700cc81f7209f514fdd7d65acbca (MD5) en
dc.description.provenance Made available in DSpace on 2013-10-08T09:31:39Z (GMT). No. of bitstreams: 1 Ali Ababaoub Lipschitz Space and Quasicionformal Mappings.pdf: 501408 bytes, checksum: ba59700cc81f7209f514fdd7d65acbca (MD5) Previous issue date: 2013 en
dc.format.mimetype PDF en_US
dc.language.iso en en_US
dc.publisher Belgrade en_US
dc.title Lipšicov prostor i kvazikonformna preslikavanja en_US
mf.author.birth-date 1963-03-28
mf.author.birth-place Sabrata en_US
mf.author.birth-country Libya en_US
mf.author.residence-state Libya en_US
mf.author.citizenship Libyan en_US
mf.author.nationality Libyan en_US
mf.subject.area Mathematics en_US
mf.subject.subarea Complex analysis en_US
mf.contributor.committee Božin, Vladimir
mf.contributor.committee Arsenović, Miloš
mf.contributor.committee Manojlović, Vesna
mf.university.faculty Mathematical en_US
mf.document.references 60 en_US
mf.document.pages 50 en_US
mf.document.location Belgrade en_US
mf.document.genealogy-project No en_US
mf.author.parent Elhrari en_US
mf.university Belgrade en_US

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