On the Problem of Plateau:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1993
|
| Schriftenreihe: | Ergebnisse der Mathematik und Ihrer Grenƶgebiete
2 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The most immediate one-dimensional variation problem is certainly the problem of determining an arc of curve, bounded by two given and having a smallest possible length. The problem of deter points mining and investigating a surface with given boundary and with a smallest possible area might then be considered as the most immediate two-dimensional variation problem. The classical work, concerned with the latter problem, is summed up in a beautiful and enthusiastic manner in DARBOUX'S Theorie generale des surfaces, vol. I, and in the first volume of the collected papers of H. A. SCHWARZ. The purpose of the present report is to give a picture of the progress achieved in this problem during the period beginning with the Thesis of LEBESGUE (1902). Our problem has always been considered as the outstanding example for the application of Analysis and Geometry to each other, and the recent work in the problem will certainly strengthen this opinion. It seems, in particular, that this recent work will be a source of inspiration to the Analyst interested in Calculus of Variations and to the Geometer interested in the theory of the area and in the theory of the conformal maps of general surfaces. These aspects of the subject will be especially emphasized in this report. The report consists of six Chapters. The first three Chapters are important tools or concerned with investigations which yielded either important ideas for the proofs of the existence theorems reviewed in the last three Chapters |
| Beschreibung: | 1 Online-Ressource (VII, 109 p) |
| ISBN: | 9783642991189 9783642983078 |
| DOI: | 10.1007/978-3-642-99118-9 |
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| 245 | 1 | 0 | |a On the Problem of Plateau |c by Tibor Radó |
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| 500 | |a The most immediate one-dimensional variation problem is certainly the problem of determining an arc of curve, bounded by two given and having a smallest possible length. The problem of deter points mining and investigating a surface with given boundary and with a smallest possible area might then be considered as the most immediate two-dimensional variation problem. The classical work, concerned with the latter problem, is summed up in a beautiful and enthusiastic manner in DARBOUX'S Theorie generale des surfaces, vol. I, and in the first volume of the collected papers of H. A. SCHWARZ. The purpose of the present report is to give a picture of the progress achieved in this problem during the period beginning with the Thesis of LEBESGUE (1902). Our problem has always been considered as the outstanding example for the application of Analysis and Geometry to each other, and the recent work in the problem will certainly strengthen this opinion. It seems, in particular, that this recent work will be a source of inspiration to the Analyst interested in Calculus of Variations and to the Geometer interested in the theory of the area and in the theory of the conformal maps of general surfaces. These aspects of the subject will be especially emphasized in this report. The report consists of six Chapters. The first three Chapters are important tools or concerned with investigations which yielded either important ideas for the proofs of the existence theorems reviewed in the last three Chapters | ||
| 650 | 4 | |a Engineering | |
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Datensatz im Suchindex
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| author | Radó, Tibor |
| author_facet | Radó, Tibor |
| author_role | aut |
| author_sort | Radó, Tibor |
| author_variant | t r tr |
| building | Verbundindex |
| bvnumber | BV042423164 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165516364 (DE-599)BVBBV042423164 |
| dewey-full | 620 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620 |
| dewey-search | 620 |
| dewey-sort | 3620 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-99118-9 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642991189 9783642983078 |
| language | English |
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| physical | 1 Online-Ressource (VII, 109 p) |
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| series2 | Ergebnisse der Mathematik und Ihrer Grenƶgebiete |
| spelling | Radó, Tibor Verfasser aut On the Problem of Plateau by Tibor Radó Berlin, Heidelberg Springer Berlin Heidelberg 1993 1 Online-Ressource (VII, 109 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und Ihrer Grenƶgebiete 2 The most immediate one-dimensional variation problem is certainly the problem of determining an arc of curve, bounded by two given and having a smallest possible length. The problem of deter points mining and investigating a surface with given boundary and with a smallest possible area might then be considered as the most immediate two-dimensional variation problem. The classical work, concerned with the latter problem, is summed up in a beautiful and enthusiastic manner in DARBOUX'S Theorie generale des surfaces, vol. I, and in the first volume of the collected papers of H. A. SCHWARZ. The purpose of the present report is to give a picture of the progress achieved in this problem during the period beginning with the Thesis of LEBESGUE (1902). Our problem has always been considered as the outstanding example for the application of Analysis and Geometry to each other, and the recent work in the problem will certainly strengthen this opinion. It seems, in particular, that this recent work will be a source of inspiration to the Analyst interested in Calculus of Variations and to the Geometer interested in the theory of the area and in the theory of the conformal maps of general surfaces. These aspects of the subject will be especially emphasized in this report. The report consists of six Chapters. The first three Chapters are important tools or concerned with investigations which yielded either important ideas for the proofs of the existence theorems reviewed in the last three Chapters Engineering Engineering, general Ingenieurwissenschaften Plateau-Problem (DE-588)4174854-2 gnd rswk-swf Subharmonische Funktion (DE-588)4183900-6 gnd rswk-swf Subharmonische Funktion (DE-588)4183900-6 s Plateau-Problem (DE-588)4174854-2 s 1\p DE-604 https://doi.org/10.1007/978-3-642-99118-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Radó, Tibor On the Problem of Plateau Engineering Engineering, general Ingenieurwissenschaften Plateau-Problem (DE-588)4174854-2 gnd Subharmonische Funktion (DE-588)4183900-6 gnd |
| subject_GND | (DE-588)4174854-2 (DE-588)4183900-6 |
| title | On the Problem of Plateau |
| title_auth | On the Problem of Plateau |
| title_exact_search | On the Problem of Plateau |
| title_full | On the Problem of Plateau by Tibor Radó |
| title_fullStr | On the Problem of Plateau by Tibor Radó |
| title_full_unstemmed | On the Problem of Plateau by Tibor Radó |
| title_short | On the Problem of Plateau |
| title_sort | on the problem of plateau |
| topic | Engineering Engineering, general Ingenieurwissenschaften Plateau-Problem (DE-588)4174854-2 gnd Subharmonische Funktion (DE-588)4183900-6 gnd |
| topic_facet | Engineering Engineering, general Ingenieurwissenschaften Plateau-Problem Subharmonische Funktion |
| url | https://doi.org/10.1007/978-3-642-99118-9 |
| work_keys_str_mv | AT radotibor ontheproblemofplateau |