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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/994| TOPOLOGICAL AND GEOMETRIC ASPECTS OF YAMABE-TYPE EQUATIONS | |
| Jurgen Julio Batalla | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| MATEMÁTICAS BÁSICAS | |
| The main subject of this thesis is devoted to studying the multiplicity and uniqueness of solutions for the Yamabe-type equations, for that, we explore the geometric and topological properties of the equation. Our most important assumption is the existence of an isoparame- tric function on a Riemannian manifold. Indeed, we classify the isoparametric functions on Rn Mm , n;m 2, with compact level sets, where Mm is a connected, closed Riemannian manifold of dimension m. Also, we classify the isoparametric hypersurfaces in S2 R2 with constant principal curvatures. On the other hand, we study positive solutions of the equation 􀀀gu + u = uq, with > 0, q > 1. If M supports a proper isoparametric function with focal varieties M1, M2 of dimension d1 d2 we show that for any q < n􀀀d2+2 n􀀀d2􀀀2 the number of positive solutions of the equation 􀀀gu + u = uq tends to 1 as ! +1. When d2 > 0 | |
| 14-05-2019 | |
| Trabajo de grado, doctorado | |
| OTRAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
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| TE 715.pdf | 408.05 kB | Adobe PDF | Visualizar/Abrir |