FU Berlin Digitale Dissertation
Dirk Christoph Franke : Quasireguläre Abbildungen und Hölder Stetigkeit für Differentialformen auf Riemannschen Mannigfaltigkeiten Quasiregular mappings and Hölder continuity of differential forms on Riemannian manifolds
|Abstract| |Table of Contents| |More Information|

Abstract With the help of the theory of differential forms this dissertation presents some well-known and also new results about quasiregular mappings on Riemannian manifolds. We consider some recently introduced classes of differential forms, the WT-classes, and show that elements of these classes are solutions of a quasilinear elliptic equation. Some differential forms composed of the components of a quasiregular mapping can be used as an example for these classes. In the second part we give a new definition for the Hölder continuity of differential forms on Riemannian manifolds and show that one of our classes fulfills this requirement.

Table of Contents Download the whole PhDthesis as a zip-tar file or as zip-File For download in PDF format click the chapter title Introduction3 Differential forms on {Imskip -hinmuskip mskip - hinmuskip R}&supn;}7 Riemannian manifolds}10 Differential forms on Riemannian manifolds}16 The {cal W}{cal T}-classes of differential forms}22 Quasilinear elliptic equations}24 Quasiregular mappings}26 A-harmonic differential forms and quasiregular mappings}28 Quasiregular mappings and {cal W}{cal T}-classes}35 Morrey´s Lemma on manifolds}40 Estimate for the energy integral}46 Hölder continuity for differential forms}53 Examples}55 References}57 Zusammenfassung (Abstract in German)60 Curriculum vitae61

More Information:
Online available:	http://www.diss.fu-berlin.de/1999/57/indexe.html
Language of PhDThesis:	english
Keywords:	quasiregular mappings, differential forms, quasilinear ellipticequations
DNB-Sachgruppe:	27 Mathematik
Classification MSC:	30C60, 58A10, 14F10, 30F30
Date of disputation:	18-Jun-1999
PhDThesis from:	Fachbereich Mathematik u. Informatik, Freie Universität Berlin
First Referee:	Prof. Dr. Ilppo Simo Louhivaara
Second Referee:	Prof. Dr. Vladimir M. Miklyukov
Third Referee:	Prof. Dr. Matti Vuorinen
Contact (Author):	franke@math.fu-berlin.de
Contact (Advisor):	miklyuk@math.byu.edu, vuorinen@csc.fi
Date created:	11-Oct-1999
Date available:	24-Aug-2000

 

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