Complete Minimal Surfaces of Finite Total Curvature:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1994
|
| Series: | Mathematics and Its Applications
294 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature. Our exposition is based upon the philosophy that the study of finite total curvature complete minimal surfaces in R3, in large measure, coincides with the study of meromorphic functions and linear series on compact Riemann sur faces. This philosophy is first indicated in the fundamental theorem of Chern and Osserman: A complete minimal surface M immersed in R3 is of finite total curvature if and only if M with its induced conformal structure is conformally equivalent to a compact Riemann surface Mg punctured at a finite set E of points and the tangential Gauss map extends to a holomorphic map Mg _ P2. Thus a finite total curvature complete minimal surface in R3 gives rise to a plane algebraic curve. Let Mg denote a fixed but otherwise arbitrary compact Riemann surface of genus g. A positive integer r is called a puncture number for Mg if Mg can be conformally immersed into R3 as a complete finite total curvature minimal surface with exactly r punctures; the set of all puncture numbers for Mg is denoted by P (M ). For example, Jorge and Meeks [JM] showed, by constructing an example g for each r, that every positive integer r is a puncture number for the Riemann surface pl |
| Physical Description: | 1 Online-Ressource (VIII, 160 p) |
| ISBN: | 9789401711043 9789048144433 |
| DOI: | 10.1007/978-94-017-1104-3 |
Staff View
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| 500 | |a This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature. Our exposition is based upon the philosophy that the study of finite total curvature complete minimal surfaces in R3, in large measure, coincides with the study of meromorphic functions and linear series on compact Riemann sur faces. This philosophy is first indicated in the fundamental theorem of Chern and Osserman: A complete minimal surface M immersed in R3 is of finite total curvature if and only if M with its induced conformal structure is conformally equivalent to a compact Riemann surface Mg punctured at a finite set E of points and the tangential Gauss map extends to a holomorphic map Mg _ P2. Thus a finite total curvature complete minimal surface in R3 gives rise to a plane algebraic curve. Let Mg denote a fixed but otherwise arbitrary compact Riemann surface of genus g. A positive integer r is called a puncture number for Mg if Mg can be conformally immersed into R3 as a complete finite total curvature minimal surface with exactly r punctures; the set of all puncture numbers for Mg is denoted by P (M ). For example, Jorge and Meeks [JM] showed, by constructing an example g for each r, that every positive integer r is a puncture number for the Riemann surface pl | ||
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| author | Yang, Kichoon |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-1104-3 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9789401711043 9789048144433 |
| language | English |
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| spelling | Yang, Kichoon Verfasser aut Complete Minimal Surfaces of Finite Total Curvature by Kichoon Yang Dordrecht Springer Netherlands 1994 1 Online-Ressource (VIII, 160 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 294 This monograph contains an exposition of the theory of minimal surfaces in Euclidean space, with an emphasis on complete minimal surfaces of finite total curvature. Our exposition is based upon the philosophy that the study of finite total curvature complete minimal surfaces in R3, in large measure, coincides with the study of meromorphic functions and linear series on compact Riemann sur faces. This philosophy is first indicated in the fundamental theorem of Chern and Osserman: A complete minimal surface M immersed in R3 is of finite total curvature if and only if M with its induced conformal structure is conformally equivalent to a compact Riemann surface Mg punctured at a finite set E of points and the tangential Gauss map extends to a holomorphic map Mg _ P2. Thus a finite total curvature complete minimal surface in R3 gives rise to a plane algebraic curve. Let Mg denote a fixed but otherwise arbitrary compact Riemann surface of genus g. A positive integer r is called a puncture number for Mg if Mg can be conformally immersed into R3 as a complete finite total curvature minimal surface with exactly r punctures; the set of all puncture numbers for Mg is denoted by P (M ). For example, Jorge and Meeks [JM] showed, by constructing an example g for each r, that every positive integer r is a puncture number for the Riemann surface pl Mathematics Geometry, algebraic Functions of complex variables Global differential geometry Crystallography Surfaces (Physics) Differential Geometry Functions of a Complex Variable Algebraic Geometry Characterization and Evaluation of Materials Mathematik Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Minimalfläche (DE-588)4127814-8 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 s Minimalfläche (DE-588)4127814-8 s 1\p DE-604 https://doi.org/10.1007/978-94-017-1104-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yang, Kichoon Complete Minimal Surfaces of Finite Total Curvature Mathematics Geometry, algebraic Functions of complex variables Global differential geometry Crystallography Surfaces (Physics) Differential Geometry Functions of a Complex Variable Algebraic Geometry Characterization and Evaluation of Materials Mathematik Algebraische Kurve (DE-588)4001165-3 gnd Minimalfläche (DE-588)4127814-8 gnd |
| subject_GND | (DE-588)4001165-3 (DE-588)4127814-8 |
| title | Complete Minimal Surfaces of Finite Total Curvature |
| title_auth | Complete Minimal Surfaces of Finite Total Curvature |
| title_exact_search | Complete Minimal Surfaces of Finite Total Curvature |
| title_full | Complete Minimal Surfaces of Finite Total Curvature by Kichoon Yang |
| title_fullStr | Complete Minimal Surfaces of Finite Total Curvature by Kichoon Yang |
| title_full_unstemmed | Complete Minimal Surfaces of Finite Total Curvature by Kichoon Yang |
| title_short | Complete Minimal Surfaces of Finite Total Curvature |
| title_sort | complete minimal surfaces of finite total curvature |
| topic | Mathematics Geometry, algebraic Functions of complex variables Global differential geometry Crystallography Surfaces (Physics) Differential Geometry Functions of a Complex Variable Algebraic Geometry Characterization and Evaluation of Materials Mathematik Algebraische Kurve (DE-588)4001165-3 gnd Minimalfläche (DE-588)4127814-8 gnd |
| topic_facet | Mathematics Geometry, algebraic Functions of complex variables Global differential geometry Crystallography Surfaces (Physics) Differential Geometry Functions of a Complex Variable Algebraic Geometry Characterization and Evaluation of Materials Mathematik Algebraische Kurve Minimalfläche |
| url | https://doi.org/10.1007/978-94-017-1104-3 |
| work_keys_str_mv | AT yangkichoon completeminimalsurfacesoffinitetotalcurvature |