An elementary proof of MinVol(Rn) = 0 for n > 3
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| Format: | Artículo científico |
| Language: | en |
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Academia Brasileira de Ciências
2008
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| _version_ | 1876478899728154624 |
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| author | Jiaqiang Mei |
| author_facet | Jiaqiang Mei |
| contents | An elementary proof of MinVol(Rn) = 0 for n > 3 Jiaqiang Mei Hongyu Wang Haifeng Xu Multidisciplinaria (Ciencias Naturales y Exactas) smooth gluing Minimal volume bounded geometry In this paper, we give an elementary proof of the result that the minimal volumes of R³ and R4 are zero. The approach is to construct a sequence of explicit complete metrics on them such that the sectional curvatures are bounded in absolute value by 1 and the volumes tend to zero. As a direct consequence, we get that MinVol (Rn) = 0 for n > 3. 2008 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32713465002 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.80 |
| format | Artículo científico |
| id | redalyc_32713465002 |
| institution | Redalyc |
| language | en |
| publishDate | 2008 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | An elementary proof of MinVol(Rn) = 0 for n > 3 Jiaqiang Mei Multidisciplinaria (Ciencias Naturales y Exactas) smooth gluing Minimal volume bounded geometry An elementary proof of MinVol(Rn) = 0 for n > 3 Jiaqiang Mei Hongyu Wang Haifeng Xu Multidisciplinaria (Ciencias Naturales y Exactas) smooth gluing Minimal volume bounded geometry In this paper, we give an elementary proof of the result that the minimal volumes of R³ and R4 are zero. The approach is to construct a sequence of explicit complete metrics on them such that the sectional curvatures are bounded in absolute value by 1 and the volumes tend to zero. As a direct consequence, we get that MinVol (Rn) = 0 for n > 3. 2008 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32713465002 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.80 |
| title | An elementary proof of MinVol(Rn) = 0 for n > 3 |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) smooth gluing Minimal volume bounded geometry |
| url | https://www.redalyc.org/articulo.oa?id=32713465002 |