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An elementary proof of MinVol(Rn) = 0 for n ≥ 3
Mei, Jiaqiang; Wang, Hongyu; Xu, Haifeng.
  • Mei, Jiaqiang; Nanjing University. Department of Mathematics. Jiangsu. CN
  • Wang, Hongyu; Yangzhou University. School of Mathematical Science. Jiangsu. CN
  • Xu, Haifeng; Yangzhou University. School of Mathematical Science. Jiangsu. CN
An. acad. bras. ciênc ; 80(4): 597-616, Dec. 2008. ilus
Article in English | LILACS | ID: lil-497107
ABSTRACT
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.
RESUMO
Neste artigo fornecemos uma demonstração elementar do resultado de que os volumes minimais de R³ e R4 são ambos iguais a zero. A abordagem consiste na construção de uma seqüência de métricas completas explícitas nesses espaços cujas curvaturas seccionais são limitadas em valor absoluto por 1 e os volumes tendem a zero. Como conseqüência direta, estabelecemos que MinVol(Rn) = 0 para n > 3.

Full text: Available Index: LILACS (Americas) Language: English Journal: An. acad. bras. ciênc Journal subject: Science Year: 2008 Type: Article / Project document Affiliation country: China Institution/Affiliation country: Nanjing University/CN / Yangzhou University/CN

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Full text: Available Index: LILACS (Americas) Language: English Journal: An. acad. bras. ciênc Journal subject: Science Year: 2008 Type: Article / Project document Affiliation country: China Institution/Affiliation country: Nanjing University/CN / Yangzhou University/CN