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Estatística
Título: MINIMAL AND CONSTANT MEAN CURVATURE EQUIVARIANT HYPERSURFACES IN S(N) AND H(N)
Autor: MARIA CLARA SCHUWARTZ FERREIRA
Colaborador(es): HENRI NICOLAS GUILLAUME ANCIAUX - Orientador
Catalogação: 18/JUL/2008 Língua(s): PORTUGUESE - BRAZIL
Tipo: TEXT Subtipo: THESIS
Notas: [pt] Todos os dados constantes dos documentos são de inteira responsabilidade de seus autores. Os dados utilizados nas descrições dos documentos estão em conformidade com os sistemas da administração da PUC-Rio.
[en] All data contained in the documents are the sole responsibility of the authors. The data used in the descriptions of the documents are in conformity with the systems of the administration of PUC-Rio.
Referência(s): [pt] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=11940&idi=1
[en] https://www.maxwell.vrac.puc-rio.br/projetosEspeciais/ETDs/consultas/conteudo.php?strSecao=resultado&nrSeq=11940&idi=2
DOI: https://doi.org/10.17771/PUCRio.acad.11940
Resumo:
In this work we study equivariant hypersurfaces in S(n) and H(n) which are minimal or have constant mean curvature. These hypersurfaces are described via a curve in S(2) and H(2) respectively, called the generating curve. In the equivariant case, the constant mean curvature equation reduces to an ODE on the generating curve, which can be reduced by one variable using the symmetry of the problem. It then turns out that this reduced system admits a first integral. In the spherical case, we find conditions insuring closedness of the integral curves, and we deduce the existence of compact hypersurfaces which are minimal or have constant mean curvature. We also discuss the question of embeddedness of these hypersurfaces. In the hyperbolic case, we limit ourselves to the minimal case. We observe that the curves are no longer closed and again we discuss embededdness.
Descrição: Arquivo:   
COVER, ACKNOWLEDGEMENTS, RESUMO, ABSTRACT, SUMMARY AND LISTS PDF    
INTRODUCTION PDF    
CHAPTER 1 PDF    
CHAPTER 2 PDF    
CHAPTER 3 PDF    
CONCLUSION PDF    
REFERENCES PDF