2012/06/30 by Nadine Große, Marc Nardmann · 5 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Constant (computer programming) #Differential geometry #Geometric Analysis and Curvature Flows #Infinity #Metric (unit) #Nonlinear Partial Differential Equations #Riemannian geometry #Space (punctuation) #Yamabe flow #math.DG #msc:53C20
paper · pdf · doi:10.1007/s12220-012-9365-6
published in Journal of Geometric Analysis 24(2), 1092-1125 (Springer Science+Business Media) · 23 pages. Lemma 10.1, Theorem 1.2 and a few minor issues corrected
arxiv created 2012/09/27 · openalex publication_date 2012/10/11 · arxiv updated 2014/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the Yamabe constant depends continuously on the Riemannian metric with respect to the fine C2-topology, and that the Yamabe constant at infinity is even locally constant with respect to this topology. We also discuss to which extent the Yamabe constant is continuous with respect to coarser topologies on the space of Riemannian metrics.