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Handbook of Teichmüller Theory, Volume VII最新文献

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Teichmüller’s work on the type problem teichm<s:1> ller对类型问题的研究
Handbook of Teichmüller Theory, Volume VII Pub Date : 2020-02-15 DOI: 10.4171/203-1/25
Vincent Alberge, Melkana Brakalova-Trevithick, A. Papadopoulos
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引用次数: 2
A commentary on Lavrentieff’s paper "Sur une classe de représentations continues" 对lavrentieff论文《论连续表现类》的评论
Handbook of Teichmüller Theory, Volume VII Pub Date : 2020-02-15 DOI: 10.4171/203-1/21
Vincent Alberge, A. Papadopoulos
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引用次数: 2
Introduction to Teichmüller theory, old and new, VII 新与旧的泰希·<s:1>勒理论导论7
Handbook of Teichmüller Theory, Volume VII Pub Date : 2020-02-15 DOI: 10.4171/203-1/1
A. Papadopoulos
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引用次数: 0
A letter 一个字母
Handbook of Teichmüller Theory, Volume VII Pub Date : 2020-02-15 DOI: 10.4171/203-1/13
Oswald Teichmüller
{"title":"A letter","authors":"Oswald Teichmüller","doi":"10.4171/203-1/13","DOIUrl":"https://doi.org/10.4171/203-1/13","url":null,"abstract":"","PeriodicalId":12912,"journal":{"name":"Handbook of Teichmüller Theory, Volume VII","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83452744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A note about Mikhaïl Lavrentieff and his world of analysis in the Soviet Union 关于Mikhaïl Lavrentieff和他在苏联的分析世界的注释
Handbook of Teichmüller Theory, Volume VII Pub Date : 2020-02-15 DOI: 10.4171/203-1/12
A. Papadopoulos, Galina Sinkevich
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引用次数: 0
Value distribution theory and Teichmüller’s paper "Einfache Beispiele zur Wertverteilungslehre" 价值分配理论和传福音》
Handbook of Teichmüller Theory, Volume VII Pub Date : 2020-01-28 DOI: 10.4171/203-1/27
Athanase Papadopoulos
{"title":"Value distribution theory and Teichmüller’s paper \"Einfache Beispiele zur Wertverteilungslehre\"","authors":"Athanase Papadopoulos","doi":"10.4171/203-1/27","DOIUrl":"https://doi.org/10.4171/203-1/27","url":null,"abstract":"This survey will appear in Vol. VII of the Handbook of Teichmuller theory (European Mathematical Society Publishing House, 2020). It is a commentary on Teichmuller's paper \"Einfache Beispiele zur Wertverteilungslehre\", published in 1944, whose English translation appears in that volume. Together with Teichmuller's paper, we survey the development of value distribution theory, in the period starting from Gauss's work on the Fundamental Theorem of Algebra and ending with the work of Teichmuller. We mention the foundational work of several mathematicians , including Picard, Laguerre, Poincare, Hadamard, Borel, Montel, Valiron, and others, and we give a quick overview of the various notions introduced by Nevanlinna and some of his results on that theory.","PeriodicalId":12912,"journal":{"name":"Handbook of Teichmüller Theory, Volume VII","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78872366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A note on Nicolas-Auguste Tissot: at the origin of quasiconformal mappings 天梭注:论拟共形映射的起源
Handbook of Teichmüller Theory, Volume VII Pub Date : 2020-01-08 DOI: 10.4171/203-1/10
A. Papadopoulos
{"title":"A note on Nicolas-Auguste Tissot: at the origin of quasiconformal mappings","authors":"A. Papadopoulos","doi":"10.4171/203-1/10","DOIUrl":"https://doi.org/10.4171/203-1/10","url":null,"abstract":"Nicolas-Auguste Tissot (1824--1897) was a French mathematician and cartographer. He introduced a tool which became known among geographers under the name ``Tissot indicatrix'', and which was widely used during the first half of the twentieth century in cartography. This is a graphical representation of a field of ellipses, indicating at each point of a geographical map the distorsion of this map, both in direction and in magnitude. Each ellipse represented at a given point is the image of an infinitesimal circle in the domain of the map (generally speaking, a sphere representing the surface of the earth) by the projection that realizes the geographical map. Tissot studied extensively, from a mathematical viewpoint, the distortion of mappings from the sphere onto the Euclidean plane, and he also developed a theory for the distorsion of mappings between general surfaces. His ideas are close to those that are at the origin of the work on quasiconformal mappings that was developed several decades after him by Gr{\"o}tzsch, Lavrentieff, Ahlfors and Teichm{\"u}ller. Gr{\"o}tzsch, in his papers, mentions the work of Tissot, and in some of the drawings he made for his articles, the Tissot indicatrix is represented. Teichm{\"u}ller mentions the name Tissot in a historical section in one of his fundamental papers in which he points out that quasiconformal mappings were initially used by geographers. The name Tissot is missing from all the known historical reports on quasiconformal mappings. In the present article, we report on this work of Tissot, showing that the theory of quasiconformal mappings has a practical origin. The final version of this article will appear in Vol. VII of the Handbook of Teichm{\"u}ller Theory (European Mathematical Society Publishing House, 2020).","PeriodicalId":12912,"journal":{"name":"Handbook of Teichmüller Theory, Volume VII","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85132805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A Commentary on Teichmüller’s paper "Untersuchungen über konforme und quasikonforme Abbildungen" 大穆勒论文的一张信件叫做“对守旧派及守旧派的研究”
Handbook of Teichmüller Theory, Volume VII Pub Date : 2019-12-24 DOI: 10.4171/203-1/26
Vincent Alberge, Melkana Brakalova-Trevithick, Athanase Papadopoulos
{"title":"A Commentary on Teichmüller’s paper \"Untersuchungen über konforme und quasikonforme Abbildungen\"","authors":"Vincent Alberge, Melkana Brakalova-Trevithick, Athanase Papadopoulos","doi":"10.4171/203-1/26","DOIUrl":"https://doi.org/10.4171/203-1/26","url":null,"abstract":"This is a commentary on Teichm{\"u}ller's paper Unter-suchungen{\"u}ber konforme und quasikonforme Abbildungen (Inves-tigations on conformal and quasiconformal mappings) published in 1938. The paper contains fundamental results in conformal geometry , in particular a lemma, known as the Modulsatz, which insures the almost circularity of certain loci defined as complementary components of simply connected regions in the Riemann sphere, and another lemma, which we call the Main Lemma, which insures the circularity near infinity of the image of circles by a qua-siconformal map. The two results find wide applications in value distribution theory, where they allow the efficient use of moduli of doubly connected domains and of quasiconformal mappings. Te-ichm{\"u}ller's paper also contains a thorough development of the theory of conformal invariants of doubly connected domains.The final version of this paper will appear in Vol. VII of the emph{Handbook of Teichm{\"u}ller theory} (European Mathematical Society Publishing House, 2020).","PeriodicalId":12912,"journal":{"name":"Handbook of Teichmüller Theory, Volume VII","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79201116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On five papers by Herbert Grötzsch 在赫伯特的五篇论文中Grötzsch
Handbook of Teichmüller Theory, Volume VII Pub Date : 2019-12-17 DOI: 10.4171/203-1/19
Vincent Alberge, A. Papadopoulos
{"title":"On five papers by Herbert Grötzsch","authors":"Vincent Alberge, A. Papadopoulos","doi":"10.4171/203-1/19","DOIUrl":"https://doi.org/10.4171/203-1/19","url":null,"abstract":"Herbert Gr{\"o}tzsch is the main founder of the theory of quasicon-formal mappings. We review five of his papers, written between 1928 and 1932, that show the progress of his work from conformal to quasiconformal geometry. This will give an idea of his motivation for introducing quasicon-formal mappings, of the problems he addressed and on the results he obtained concerning these mappings. The final version of this paper will appear in Vol. VII of the Handbook of Teichm{\"u}ller theory.","PeriodicalId":12912,"journal":{"name":"Handbook of Teichmüller Theory, Volume VII","volume":"127 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75838948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Holomorphic quadratic differentials in Teichmüller theory teichm<s:1> ller理论中的全纯二次微分
Handbook of Teichmüller Theory, Volume VII Pub Date : 2019-02-18 DOI: 10.4171/203-1/4
Subhojoy Gupta
{"title":"Holomorphic quadratic differentials in Teichmüller theory","authors":"Subhojoy Gupta","doi":"10.4171/203-1/4","DOIUrl":"https://doi.org/10.4171/203-1/4","url":null,"abstract":"This expository survey describes how holomorphic quadratic differentials arise in several aspects of Teichm\"uller theory, highlighting their relation with various geometric structures on surfaces. The final section summarizes results for non-compact surfaces of finite type, when the quadratic differential has poles of finite order at the punctures.","PeriodicalId":12912,"journal":{"name":"Handbook of Teichmüller Theory, Volume VII","volume":"100 S397","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91416470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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