Calculus of Variations and Geometric Measure Theory

G. Ciraolo - A. Figalli - F. Maggi

A quantitative analysis of metrics on $\mathbb R^n$ with almost constant positive scalar curvature, with applications to fast diffusion flows

created by maggi on 05 Feb 2016
modified by figalli on 19 Aug 2024

[BibTeX]

Published Paper

Inserted: 5 feb 2016
Last Updated: 19 aug 2024

Journal: Int. Math. Res. Not. IMRN
Pages: 31
Year: 2018

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.


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