Please use this identifier to cite or link to this item: 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 &#1048576;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&#1048576;d2+2 n&#1048576;d2&#1048576;2 the number of positive solutions of the equation &#1048576;gu + u = uq tends to 1 as ! +1. When d2 > 0
14-05-2019
Trabajo de grado, doctorado
OTRAS
Versión aceptada
acceptedVersion - Versión aceptada
Appears in Collections:Tesis del CIMAT

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