Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Wiesbaden
Vieweg+Teubner Verlag
1993
|
| Schriftenreihe: | Aspects of Mathematics
21 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | These notes are based on lectures given at Instituto de Matematica e Esta tistica in Universidade de Sao Paulo in the spring of 1990. The main sub ject is function-theoretic, particularly, value-distribution-theoretic proper ties of the Gauss maps of minimal surfaces in the euclidean space. The classical Bernstein theorem asserts that there is no nonfiat min 2 imal surface in R3 which is described as the graph of a C -function on R2. On the other hand, the classical Liouville theorem asserts that there is no bounded nonconstant holomorphic function on the complex plane. The conclusions of these theorems have a strong resemblance. Bernstein's theorem was improved by many reseachers in the field of differential ge ometry, Heinz, Hopf, Nitsche, Osserman, Chern and others. On the other hand, in the field of function theory, Liouville's theorem was improved as the Casoratti-Weierstrass theorem, Picard's theorem and Nevanlinna theory, which were generalized to the case of holomorphic curves in the projective space by E. Borel, H. C art an , J. and H. Weyl and L. V. Ahlfors |
| Beschreibung: | 1 Online-Ressource (XIII, 208 p) |
| ISBN: | 9783322802712 9783322802736 |
| ISSN: | 0179-2156 |
| DOI: | 10.1007/978-3-322-80271-2 |
Internformat
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| 245 | 1 | 0 | |a Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm |c by Hirotaka Fujimoto |
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| 500 | |a These notes are based on lectures given at Instituto de Matematica e Esta tistica in Universidade de Sao Paulo in the spring of 1990. The main sub ject is function-theoretic, particularly, value-distribution-theoretic proper ties of the Gauss maps of minimal surfaces in the euclidean space. The classical Bernstein theorem asserts that there is no nonfiat min 2 imal surface in R3 which is described as the graph of a C -function on R2. On the other hand, the classical Liouville theorem asserts that there is no bounded nonconstant holomorphic function on the complex plane. The conclusions of these theorems have a strong resemblance. Bernstein's theorem was improved by many reseachers in the field of differential ge ometry, Heinz, Hopf, Nitsche, Osserman, Chern and others. On the other hand, in the field of function theory, Liouville's theorem was improved as the Casoratti-Weierstrass theorem, Picard's theorem and Nevanlinna theory, which were generalized to the case of holomorphic curves in the projective space by E. Borel, H. C art an , J. and H. Weyl and L. V. Ahlfors | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-322-80271-2 |
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| isbn | 9783322802712 9783322802736 |
| issn | 0179-2156 |
| language | English |
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| spelling | Fujimoto, Hirotaka Verfasser aut Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm by Hirotaka Fujimoto Wiesbaden Vieweg+Teubner Verlag 1993 1 Online-Ressource (XIII, 208 p) txt rdacontent c rdamedia cr rdacarrier Aspects of Mathematics 21 0179-2156 These notes are based on lectures given at Instituto de Matematica e Esta tistica in Universidade de Sao Paulo in the spring of 1990. The main sub ject is function-theoretic, particularly, value-distribution-theoretic proper ties of the Gauss maps of minimal surfaces in the euclidean space. The classical Bernstein theorem asserts that there is no nonfiat min 2 imal surface in R3 which is described as the graph of a C -function on R2. On the other hand, the classical Liouville theorem asserts that there is no bounded nonconstant holomorphic function on the complex plane. The conclusions of these theorems have a strong resemblance. Bernstein's theorem was improved by many reseachers in the field of differential ge ometry, Heinz, Hopf, Nitsche, Osserman, Chern and others. On the other hand, in the field of function theory, Liouville's theorem was improved as the Casoratti-Weierstrass theorem, Picard's theorem and Nevanlinna theory, which were generalized to the case of holomorphic curves in the projective space by E. Borel, H. C art an , J. and H. Weyl and L. V. Ahlfors Mathematics Geometry Mathematik Minimalfläche (DE-588)4127814-8 gnd rswk-swf Gauß-Abbildung (DE-588)4156105-3 gnd rswk-swf Holomorphe Kurve (DE-588)4160476-3 gnd rswk-swf Wertverteilungstheorie (DE-588)4137510-5 gnd rswk-swf Holomorphe Kurve (DE-588)4160476-3 s Wertverteilungstheorie (DE-588)4137510-5 s Minimalfläche (DE-588)4127814-8 s Gauß-Abbildung (DE-588)4156105-3 s 1\p DE-604 https://doi.org/10.1007/978-3-322-80271-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fujimoto, Hirotaka Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm Mathematics Geometry Mathematik Minimalfläche (DE-588)4127814-8 gnd Gauß-Abbildung (DE-588)4156105-3 gnd Holomorphe Kurve (DE-588)4160476-3 gnd Wertverteilungstheorie (DE-588)4137510-5 gnd |
| subject_GND | (DE-588)4127814-8 (DE-588)4156105-3 (DE-588)4160476-3 (DE-588)4137510-5 |
| title | Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm |
| title_auth | Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm |
| title_exact_search | Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm |
| title_full | Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm by Hirotaka Fujimoto |
| title_fullStr | Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm by Hirotaka Fujimoto |
| title_full_unstemmed | Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm by Hirotaka Fujimoto |
| title_short | Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm |
| title_sort | value distribution theory of the gauss map of minimal surfaces in rm |
| topic | Mathematics Geometry Mathematik Minimalfläche (DE-588)4127814-8 gnd Gauß-Abbildung (DE-588)4156105-3 gnd Holomorphe Kurve (DE-588)4160476-3 gnd Wertverteilungstheorie (DE-588)4137510-5 gnd |
| topic_facet | Mathematics Geometry Mathematik Minimalfläche Gauß-Abbildung Holomorphe Kurve Wertverteilungstheorie |
| url | https://doi.org/10.1007/978-3-322-80271-2 |
| work_keys_str_mv | AT fujimotohirotaka valuedistributiontheoryofthegaussmapofminimalsurfacesinrm |