Minimal Hypersurfaces
Mostrando 13-18 de 18 artigos, teses e dissertações.
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13. MINIMAL AND CONSTANT MEAN CURVATURE EQUIVARIANT HYPERSURFACES IN S(N) AND H(N) / HIPERSUPERFÍCIES EQUIVARIANTES MÍNIMAS E COM CURVATURA MÉDIA CONSTANTE EM S(N) E H(N)
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 varia
Publicado em: 2007
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14. The structure of weakly stable minimal hypersurfaces
Neste trabalho, anunciamos resultados de nossa investigação sobre a estrutura das hipersuperfícies mínimas completas e fracamente estáveis em um espaço ambiente de curvatura seccional não-negativa. Em particular, uma hipersuperfície mínima orientável completa e estável em Rm, m > 4, possui apenas um fim, e uma superfície mínima completa orientá
Anais da Academia Brasileira de Ciências. Publicado em: 2006-06
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15. Simetrias de hipersuperfÃcies com curvatura escalar nula via PrincÃpio da TangÃncia
In 1983, R. Schoen proved that the only complete immersed minimal hypersurfaces in Rn+1 with two regular ends are the catenoid and a pair of planes. The methods used by Schoen led J. Hounie and M. L. Leite to prove a similar result for hypersurfaces with zero scalar curvature. The main difference in the proof of the two theorems is in the fact that the equat
Publicado em: 2005
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16. The boundary value problem for maximal hypersurfaces
A spacelike hypersurface (condimension 1) in a Lorentzian manifold is called a maximal surface if it extremizes the hypervolume functional. Although maximal surfaces are superficially analogous to minimal hypersurfaces in Riemannian geometry, their properties can be dramatically different, as can be seen from the validity of Bernstein's theorem in all dimens
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17. A remark on minimal hypercones
Let M be a minimal hypersurface in the sphere. It is shown that if the cone over M is a stable critical point for the area functional, then M admits a conformally equivalent metric with positive scalar curvature. This gives both topological and geometric restrictions on such hypersurfaces M.
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18. A New Proof of the Interior Gradient Bound for the Minimal Surface Equation in n Dimensions
An interior gradient bound for classical solutions of the minimal surface equation in n variables was established by Bombieri, De Giorgi, and Miranda in 1968. We provide a new and simpler derivation of this estimate and partly develop in the process some new techniques applicable to the study of hypersurfaces in general.