Simetrias de hipersuperfÃcies com curvatura escalar nula via PrincÃpio da TangÃncia

AUTOR(ES)

Almir RogÃrio Silva Santos

DATA DE PUBLICAÇÃO

2005

RESUMO

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 equation for zero mean curvature is always elliptic, which does not always happen for the equation for zero scalar curvature. Hence the need for additional hypothesis in the version for zero scalar curvature, namely that the next curvature function H3 does not vanish. In this work we present the basic tools for proving the Hounie-Leite Theorem, namely the Maximum Principle for elliptic equations, the Tangency Principle for hypersurfaces with vanishing intermediate curvature and a reflection principle for hypersurfaces with vanishing intermediate. We also present the proof of Hounie-Leite Theorem

ASSUNTO(S)

hipersuperfÃcie matematica curvatura escalar nula hypersurfaces princÃpio da tangÃncia tangency principle zero scalar curvature

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