Abstract:
We showed the existence of non-radial solutions of the equation δu - λu + λuq = 0 on the round sphere Sm, for q < (m+2)/(m-2), and study the number of such solutions in terms of λ. We show that for any isoparametric hypersurface M ⊂ Sm there are solutions such that M is a regular level set (and the number of such solutions increases with λ). We also show similar results for isoparametric hypersurfaces in general Riemannian manifolds. These solutions give multiplicity results for metrics of constant scalar curvature on conformal classes of Riemannian products. © 2014 International Press.
Registro:
Documento: |
Artículo
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Título: | Isoparametric hypersurfaces and metrics of constant scalar curvature |
Autor: | Henry, G.; Petean, J. |
Filiación: | Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I., Buenos Aires, C1428EHA, Argentina CIMAT, A.P. 402, Guanajuato. Gto., 36000, Mexico
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Palabras clave: | Isoparametric hypersurfaces; Yamabe equation |
Año: | 2014
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Volumen: | 18
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Número: | 1
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Página de inicio: | 53
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Página de fin: | 68
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DOI: |
http://dx.doi.org/10.4310/AJM.2014.v18.n1.a3 |
Título revista: | Asian Journal of Mathematics
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Título revista abreviado: | Asian J. Math.
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ISSN: | 10936106
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10936106_v18_n1_p53_Henry |
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Citas:
---------- APA ----------
Henry, G. & Petean, J.
(2014)
. Isoparametric hypersurfaces and metrics of constant scalar curvature. Asian Journal of Mathematics, 18(1), 53-68.
http://dx.doi.org/10.4310/AJM.2014.v18.n1.a3---------- CHICAGO ----------
Henry, G., Petean, J.
"Isoparametric hypersurfaces and metrics of constant scalar curvature"
. Asian Journal of Mathematics 18, no. 1
(2014) : 53-68.
http://dx.doi.org/10.4310/AJM.2014.v18.n1.a3---------- MLA ----------
Henry, G., Petean, J.
"Isoparametric hypersurfaces and metrics of constant scalar curvature"
. Asian Journal of Mathematics, vol. 18, no. 1, 2014, pp. 53-68.
http://dx.doi.org/10.4310/AJM.2014.v18.n1.a3---------- VANCOUVER ----------
Henry, G., Petean, J. Isoparametric hypersurfaces and metrics of constant scalar curvature. Asian J. Math. 2014;18(1):53-68.
http://dx.doi.org/10.4310/AJM.2014.v18.n1.a3