A Quantitative Analysis of Metrics on $\mathbb{R}^n$ with Almost Constant Positive Scalar Curvature, with Applications to Fast Diffusion Flows. (5th May 2017)

• Record Type: Journal Article
• Authors: Ciraolo, Giulio; Figalli, Alessio; Maggi, Francesco
• Is Part Of: International mathematics research notices. Volume 2018:Number 21(2018)
• Page Start: 6780
• Page End: 6797
• Publication Date: 2017-05-05
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx071
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: We prove a quantitative structure theorem for metrics on $\mathbb{R}^n$ that are conformal to the flat metric, have almost constant positive scalar curvature, and cannot concentrate more than one bubble. As an application of our result, we show a quantitative rate of convergence in relative entropy for a fast diffusion equation in $\mathbb{R}^n$ related to the Yamabe flow.