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Doctoral Thesis
DOI
10.11606/T.45.2016.tde-30082016-001339
Document
Author
Full name
Elkin Dario Cardenas Diaz
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2016
Supervisor
Committee
Piccione, Paolo (President)
Manfio, Fernando
Mercuri, Francesco
Montenegro, Marcelo da Silva
Siciliano, Gaetano
Title in Portuguese
Fenômeno de bifurcação no problema de Yamabe sobre variedades riemannianas com bordo
Keywords in Portuguese
Bifurcação
Classes conforme
Métricas riemannianas
Problema de Yamabe
Variedades produto
Abstract in Portuguese
No presente trabalho consideramos o produto de uma variedade Riemanniana compacta sem bordo de curvatura escalar zero e uma variedade Riemanniana compacta com bordo, curvatura escalar zero e curvatura media constante no bordo, e fazemos uso da teoria de bifurcação para provar a existência de um numero infinito de classes conforme com, pelo menos, duas métricas Riemannianas não homotéticas de curvatura escalar zero e curvatura média constante no bordo, sobre a variedade produto.
Title in English
Phenomenon of bifurcation in Yamabe problem on Riemannian manifolds with boundary
Keywords in English
Bifurcation
Conformal class
Product manifolds
Riemannian metrics
Yamabe problem
Abstract in English
In this work, we consider the product of a compact Riemannian manifold without boundary, null scalar curvature and a compact Riemannian manifold with boundary, null scalar curvature and constant mean curvature on the boundary and we use the bifurcation theory to prove the existence of a infinite number of conformal classes with at least two non homothetic Riemannian metrics of null scalar curvature and constant mean curvature of the boundary on the product manifold.
 
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Fenomenodebifurcacao.pdf (901.70 Kbytes)
Publishing Date
2016-09-09
 
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