A generic multiplicity result for a Yamabe-type equation via Morse theory

• Ano de defesa: 2020
• Autor(a) principal: Ramos, Gustavo de Paula
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Critical point theory; Curvatura escalar; Morse theory; Nondegenerate critical points; Pontos críticos não-degenerados; Problema de Yamabe; Scalar curvature; Teoria de Morse; Teoria dos pontos críticos; Yamabe problem
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-06082020-141230/

Let M^n be a closed manifold with n>=3 and (N, h) be a Riemannian manifold with positive constant scalar curvature. We prove that a PDE similar to the Yamabe equation on the Riemannian product (MxN,g+h\\epsilon^2) depending only on conformal factors u\\colon M \\to \\mathbb has at least P_1(M) positive solutions with small energy for generic (\\epsilon,g), where \\epsilon>0 is sufficiently small and g is a Riemannian metric of class C^k on M, 2<=k<\\infty. This result is obtained by adapting techniques employed by Micheletti & Pistoia (2009), Ghimenti & Micheletti (2011) and Jimmy Petean (2016).