Isoparametric hypersurfaces and metrics of constant scalar curvature
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 (a...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10936106_v18_n1_p53_Henry |
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todo:paper_10936106_v18_n1_p53_Henry2023-10-03T16:05:01Z Isoparametric hypersurfaces and metrics of constant scalar curvature Henry, G. Petean, J. Isoparametric hypersurfaces Yamabe equation 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. Fil:Henry, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Petean, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. SER info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10936106_v18_n1_p53_Henry |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Isoparametric hypersurfaces Yamabe equation |
| spellingShingle |
Isoparametric hypersurfaces Yamabe equation Henry, G. Petean, J. Isoparametric hypersurfaces and metrics of constant scalar curvature |
| topic_facet |
Isoparametric hypersurfaces Yamabe equation |
| description |
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. |
| format |
SER |
| author |
Henry, G. Petean, J. |
| author_facet |
Henry, G. Petean, J. |
| author_sort |
Henry, G. |
| title |
Isoparametric hypersurfaces and metrics of constant scalar curvature |
| title_short |
Isoparametric hypersurfaces and metrics of constant scalar curvature |
| title_full |
Isoparametric hypersurfaces and metrics of constant scalar curvature |
| title_fullStr |
Isoparametric hypersurfaces and metrics of constant scalar curvature |
| title_full_unstemmed |
Isoparametric hypersurfaces and metrics of constant scalar curvature |
| title_sort |
isoparametric hypersurfaces and metrics of constant scalar curvature |
| url |
http://hdl.handle.net/20.500.12110/paper_10936106_v18_n1_p53_Henry |
| work_keys_str_mv |
AT henryg isoparametrichypersurfacesandmetricsofconstantscalarcurvature AT peteanj isoparametrichypersurfacesandmetricsofconstantscalarcurvature |
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1807321175004545024 |