Use este identificador para citar ou linkar para este item: http://www.repositorio.ufc.br/handle/riufc/3796
Título: On stability of cones in R{n+1} with zero scalar curvature
Autor(es): Barbosa, João Lucas Marques
Carmo, Manfredo Perdigão do
Palavras-chave: Hipersuperfícies
Curvatura
Data do documento: 2005
Editor: Annals of Global Analysis and Geometry
Citação: BARBOSA, J. L. M. ; CARMO, M. P.(2005)
Abstract: In this work we generalize the case of scalar curvature zero the results of Simmons (Ann. Math. 88 (1968), 62–105) for minimal cones in Rn+1. If Mn−1 is a compact hypersurface of the sphere Sn(1) we represent by C(M)ε the truncated cone based on M with center at the origin. It is easy to see that M has zero scalar curvature if and only if the cone base on M also has zero scalar curvature. Hounie and Leite (J. Differential Geom. 41 (1995), 247–258) recently gave the conditions for the ellipticity of the partial differential equation of the scalar curvature. To show that, we have to assume n ≥ 4 and the three-curvature of M to be different from zero. For such cones, we prove that, for n ≤ 7 there is an ε for which the truncate cone C(M)ε is not stable. We also show that for n ≥ 8 there exist compact, orientable hypersurfaces Mn−1 of the sphere with zero scalar curvature and S3 different from zero, for which all truncated cones based on M are stable.
Descrição: BARBOSA, João Lucas Marques ; CARMO, Manfredo Perdigão do. On stability of cones in R{n+1} with zero scalar curvature. Annals of Global Analysis and Geometry, v. 28, p. 107-122, 2005.
URI: http://www.repositorio.ufc.br/handle/riufc/3796
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