Use este identificador para citar ou linkar para este item: http://www.repositorio.ufc.br/handle/riufc/3832
Título: On the index of constant mean curvature 1 surfaces in hyperbolic space
Autor(es): Lima, Levi Lopes de
Rossman, Wayne
Palavras-chave: Superfícies mínimas
Espaços hiperbólicos
Data do documento: 1998
Editor: Indiana University Mathematics Journal
Citação: LIMA, L. L. ; ROSSMAN, W. (1998)
Abstract: We show that the index of a constant mean curvature 1 surface in hyperbolic 3-space is completely determined by the compact Riemann surface and secondary Gauss map that represent it in Bryant’s Weierstrass representation. We give three applications of this observation. Firstly, it allows us to explicitly compute the index of the catenoid cousins and some other examples. Secondly, it allows us to be able to apply a method similar to that of Choe (using Killing vector fields on minimal surfaces in Euclidean 3-space) to our case as well, resulting in lower bounds of index for other examples.And thirdly, it allows us to give a more direct proof of the result by do Carmo and Silveira that if a constant mean curvature 1 surface in hyperbolic 3-space has finite total curvature, then it has finite index. Finally, we show that for any constant mean curvature 1 surface in hyperbolic 3-space that has been constructed via a correspondence to a minimal surface in Euclidean 3-space, we can take advantage of this correspondence to find a lower bound for its index.
Descrição: LIMA, Levi Lopes de ; ROSSMAN, Wayne. On the index of constant mean curvature 1 surfaces in hyperbolic space. Indiana University Mathematics Journal, Bloomington, Indiana, v. 47, n. 2, p. 685-723, 1998.
URI: http://www.repositorio.ufc.br/handle/riufc/3832
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