Harmonic mappings in the plane:
Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by diff...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2004
|
| Schriftenreihe: | Cambridge tracts in mathematics
156 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 Volltext |
| Zusammenfassung: | Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 Online-Ressource (xii, 212 Seiten) |
| ISBN: | 9780511546600 |
| DOI: | 10.1017/CBO9780511546600 |
Internformat
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| 490 | 0 | |a Cambridge tracts in mathematics |v 156 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 520 | |a Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry | ||
| 650 | 4 | |a Harmonic maps | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Duren, Peter L. 1935-2020 |
| author_GND | (DE-588)135675502 |
| author_facet | Duren, Peter L. 1935-2020 |
| author_role | aut |
| author_sort | Duren, Peter L. 1935-2020 |
| author_variant | p l d pl pld |
| building | Verbundindex |
| bvnumber | BV043941653 |
| classification_rvk | SK 370 SK 700 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511546600 (OCoLC)850628623 (DE-599)BVBBV043941653 |
| dewey-full | 514/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
| dewey-sort | 3514 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511546600 |
| format | Electronic eBook |
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| id | DE-604.BV043941653 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511546600 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350623 |
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| physical | 1 Online-Ressource (xii, 212 Seiten) |
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| publishDate | 2004 |
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| spelling | Duren, Peter L. 1935-2020 Verfasser (DE-588)135675502 aut Harmonic mappings in the plane Peter Duren Cambridge Cambridge University Press 2004 1 Online-Ressource (xii, 212 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 156 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry Harmonic maps Ebene (DE-588)4150968-7 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 s Ebene (DE-588)4150968-7 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-64121-0 https://doi.org/10.1017/CBO9780511546600 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Duren, Peter L. 1935-2020 Harmonic mappings in the plane Harmonic maps Ebene (DE-588)4150968-7 gnd Harmonische Abbildung (DE-588)4023452-6 gnd |
| subject_GND | (DE-588)4150968-7 (DE-588)4023452-6 |
| title | Harmonic mappings in the plane |
| title_auth | Harmonic mappings in the plane |
| title_exact_search | Harmonic mappings in the plane |
| title_full | Harmonic mappings in the plane Peter Duren |
| title_fullStr | Harmonic mappings in the plane Peter Duren |
| title_full_unstemmed | Harmonic mappings in the plane Peter Duren |
| title_short | Harmonic mappings in the plane |
| title_sort | harmonic mappings in the plane |
| topic | Harmonic maps Ebene (DE-588)4150968-7 gnd Harmonische Abbildung (DE-588)4023452-6 gnd |
| topic_facet | Harmonic maps Ebene Harmonische Abbildung |
| url | https://doi.org/10.1017/CBO9780511546600 |
| work_keys_str_mv | AT durenpeterl harmonicmappingsintheplane |