Mestrado em Matemática (IME)
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Navegando Mestrado em Matemática (IME) por Por Orientador "FERREIRA, Walterson Pereira"
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Item Sobre uma caracterização de pequena calota esférica(Universidade Federal de Goiás, 2011-02-18) DIAS, Diogo Gonçalves; FERREIRA, Walterson Pereira; http://lattes.cnpq.br/9150818921025647It is known that small spherical caps are the only compact surfaces with constant mean curvature H 6= 0 graphics whose boundary is a round circle. This characterization is a partial answer to one of the conjectures of the spherical cap and its classic demonstration involves the Maximum Principle for surfaces with constant mean curvature. What we re doing this work is to give a new proof for this characterization of small spherical cap without the use of the Principle of Maximum. In addition, we make statements alternatives other results related to Conjecture, whenever possible.Item Superfícies de Weingarten Lineares Hiperbólicas em R3(Universidade Federal de Goiás, 2009-08-25) GUEDES, Luciene Viana; FERREIRA, Walterson Pereira; http://lattes.cnpq.br/9150818921025647The present work has been based by the [1] from Juan A. Aledo S´anches and Jos´e M. Espinar and [2] from Rafael L´opez articles. In those articles they studied hiperbolic linear Weingarten surfaces in R3 space, this is, surface whose mean curvature H and Gaussian curvature K satisfy a relation of the form aH+bK =c, where a, b, c 2 R. A such surface is said to be hiperbolic when the discriminant D := a2+4bc < 0.We obtain a representation for rotational hyperbolic linear Weingarten surfaces in terms of its Gauss map and we also present, in the case a 6= 0, a classification of linearWeingarten surfaces of hyperbolic rotation. As a consequence we obtain, in the case a 6=0, a family of complete hyperbolic linear Weingarten surfaces in R3. This contrasts with Hilbert s theorem that there do not exist complete surfaces with constant negative Gaussian curvature immersed in R3.