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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

HipersuperfÃcies r-mÃnimas com dois fins regulares

Antonio Fernando Pereira de Sousa 28 March 2008 (has links)
Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Seja Mn uma hipersuperficie r&#8722;minima de Rn+1, ou seja, suponha que M tem curvatura S r+1 identicamente nula. M Ã dita regular se fora de algum compacto M Ã a uniÃo disjunta de um nÃmero finito de fins, cada um deles regular, isto Ã, com o mesmo comportamento assintÃtico de uma hipersuperfÃcie rotacional. Mostramos que hipersuperfÃcies r-mÃnimas elipticas e mergulhadas no espaÃo Euclidiano Rn+1, 3/2(r + 1) n < 2(r + 1), com dois fins, ambos regulares, sÃo catenÃides (i.e. hipersuperfÃcies rotacionais). Isto estende resultados prÃvios apresentadospor Schoen [7] e Hounie-Leite [3]. / Let Mn be a r-minimal hypersurface in Rn+1, i.e., suppose M has curvature S r+1 identically zero. M is said regular if out of any compact M is the disjunct union of a finite number of ends, each regular, i.e., with the same assymptotic behavior that a rotational hypersurface. It is shown that embedded, elliptic rminimal hypersurfaces in Euclidean space Rn+1, 3/2 (r + 1) n < 2(r + 1), with two ends, both regular, are catenoids (i.e. rotational hypersurfaces). This extendsprevious results by Schoen [7] and Hounie-Leite [3].

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