The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature
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| Natura: | Artículo científico |
| Lingua: | en |
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Academia Brasileira de Ciências
2013
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| _version_ | 1876451354333937664 |
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| author | PEDRO A. HINOJOSA |
| author_facet | PEDRO A. HINOJOSA |
| contents | The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature PEDRO A. HINOJOSA GILVANEIDE N. SILVA Multidisciplinaria (Ciencias Naturales y Exactas) Gauss map minimal surfaces Finite total curvature Image of the Gauss map In this paper we are concerned with the image of the normal Gauss map of a minimal surface immersed in R 3 with finite total curvature. We give a different proof of the following theorem of R. Osserman: The normal Gauss map of a minimal surface immersed in R 3 with finite total curvature, which is not a plane, omits at most three points o f S 2 . Moreover, under an additional hypothesis on the type of ends, we prove that this number is exactly 2. 2013 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32729375002 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.4 Vol.85 |
| format | Artículo científico |
| id | redalyc_32729375002 |
| institution | Redalyc |
| language | en |
| publishDate | 2013 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature PEDRO A. HINOJOSA Multidisciplinaria (Ciencias Naturales y Exactas) Gauss map minimal surfaces Finite total curvature Image of the Gauss map The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature PEDRO A. HINOJOSA GILVANEIDE N. SILVA Multidisciplinaria (Ciencias Naturales y Exactas) Gauss map minimal surfaces Finite total curvature Image of the Gauss map In this paper we are concerned with the image of the normal Gauss map of a minimal surface immersed in R 3 with finite total curvature. We give a different proof of the following theorem of R. Osserman: The normal Gauss map of a minimal surface immersed in R 3 with finite total curvature, which is not a plane, omits at most three points o f S 2 . Moreover, under an additional hypothesis on the type of ends, we prove that this number is exactly 2. 2013 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32729375002 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.4 Vol.85 |
| title | The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) Gauss map minimal surfaces Finite total curvature Image of the Gauss map |
| url | https://www.redalyc.org/articulo.oa?id=32729375002 |