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Harmonic maps into trees and graphs: analytical and numerical aspects

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Bibliographic Details
Main Author:	Hesse, Martin 1973- (Author)
Format:	Thesis/Dissertation Book
Language:	English
Published:	Bonn 2004 [erschienen] 2005
Series:	Bonner mathematische Schriften 370
Subjects:	Dirichlet forms Harmonic maps Harmonische Abbildung Maßraum Graph Dirichlet-Problem Hochschulschrift
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014593819&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	100 S. Ill.

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adam_text	Titel: Harmonic maps into trees and graphs Autor: Hesse, Martin Jahr: 2005 Contents Introduction 1 1 Spiders 7 1.1 Nonlinear Energy................................. 9 1.2 Nonlinear Dirichlet Problem........................... 11 1.3 Nonlinear Dirichlet Problem for Polygonal Domains in IR2.......... 14 1.3.1 Discrete Nonlinear Dirichlet Problem.................. 15 1.3.2 Extending Maps on Vertices to Maps on the Domain......... 20 1.3.3 Convergence................................ 24 1.3.4 Numerical Results ............................ 29 1.4 Proof of Theorem 1.3............................... 31 1.5 Generalizations to Spiders with a Countable Number of Edges........ 36 2 Trees 38 2.1 Nonlinear Energy................................. 41 2.1.1 Other Definitions of Nonlinear Energy ................. 45 2.1.2 Decomposition of the Energy from Korevaar/Schoen ......... 47 2.1.3 Special Case that m is a Finite Measure ................ 54 2.2 Nonlinear Dirichlet Problem........................... 56 2.3 Nonlinear Dirichlet Problem for Polygonal Domains in K2.......... 56 2.3.1 Discrete Nonlinear Dirichlet Problem.................. 57 2.3.2 Barycenters on Finite Trees....................... 58 2.3.3 Extending Maps on Vertices to Maps on the Domain......... 61 2.3.4 Convergence................................ 66 2.4 Proof of Theorem 2.7............................... 72 2.5 Generalizations to Trees with a Countable Number of Edges......... 77 3 Graphs 79 3.1 Nonlinear Energy for Equivariant Maps..................... 81 3.1.1 Nonlinear Dirichlet Problem for Equivariant Maps........... 86 3.2 Nonlinear Energy for Maps with Values in Finite Graphs........... 88 3.2.1 Nonlinear Dirichlet Problem....................... 89 3.2.2 Homotopy Problems........................... 90 ii Contents Appendix 95 A. 1 Locality for Regular Dirichlet Forms ...................... 95 Bibliography 98
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spellingShingle	Hesse, Martin 1973- Harmonic maps into trees and graphs analytical and numerical aspects Bonner mathematische Schriften Dirichlet forms Harmonic maps Harmonische Abbildung (DE-588)4023452-6 gnd Maßraum (DE-588)4169057-6 gnd Graph (DE-588)4021842-9 gnd Dirichlet-Problem (DE-588)4129762-3 gnd
subject_GND	(DE-588)4023452-6 (DE-588)4169057-6 (DE-588)4021842-9 (DE-588)4129762-3 (DE-588)4113937-9
title	Harmonic maps into trees and graphs analytical and numerical aspects
title_auth	Harmonic maps into trees and graphs analytical and numerical aspects
title_exact_search	Harmonic maps into trees and graphs analytical and numerical aspects
title_full	Harmonic maps into trees and graphs analytical and numerical aspects vorgelegt von Martin Hesse
title_fullStr	Harmonic maps into trees and graphs analytical and numerical aspects vorgelegt von Martin Hesse
title_full_unstemmed	Harmonic maps into trees and graphs analytical and numerical aspects vorgelegt von Martin Hesse
title_short	Harmonic maps into trees and graphs
title_sort	harmonic maps into trees and graphs analytical and numerical aspects
title_sub	analytical and numerical aspects
topic	Dirichlet forms Harmonic maps Harmonische Abbildung (DE-588)4023452-6 gnd Maßraum (DE-588)4169057-6 gnd Graph (DE-588)4021842-9 gnd Dirichlet-Problem (DE-588)4129762-3 gnd
topic_facet	Dirichlet forms Harmonic maps Harmonische Abbildung Maßraum Graph Dirichlet-Problem Hochschulschrift
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volume_link	(DE-604)BV000001610
work_keys_str_mv	AT hessemartin harmonicmapsintotreesandgraphsanalyticalandnumericalaspects

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