Nesta quarta-feira, dia 25/11/2020 às 14:00, teremos a 14ª edição dos Webinários de Matemática do PPGMat – UFRGS. É com prazer que convidamos a todos. Sintam-se à vontade para compartilhar esta mensagem.
Nossos primeiros webinários já se encontram no YouTube, no canal do PPGMat. Confiram lá! 🙂
Informações do webinário desta semana:
Quantitative stability for minimizing Yamabe metrics
por Robin Neumayer (Northwestern University)
Data e hora: Quarta-feira, 25 de Novembro de 2020 às 14:00
Acesso: Plataforma Google Meet em https://meet.google.com/mis-hsdx-aqh
Resumo: The Yamabe problem asks whether, given a closed Riemannian manifold, one can find a conformal metric of constant scalar curvature (CSC). An affirmative answer was given by Schoen in 1984, following contributions from Yamabe, Trudinger, and Aubin, by establishing the existence of a function that minimizes the so-called Yamabe energy functional; the minimizing function corresponds to the conformal factor of the CSC metric.
We address the quantitative stability of minimizing Yamabe metrics. On any closed Riemannian manifold we show—in a quantitative sense—that if a function nearly minimizes the Yamabe energy, then the corresponding conformal metric is close to a CSC metric. Generically, this closeness is controlled quadratically by the Yamabe energy deficit. However, we construct an example demonstrating that this quadratic estimate is false in the general. This is joint work with Max Engelstein and Luca Spolaor and will be accessible to a general graduate student audience.