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

Giulio Ciraolo; Alessio Figalli; Francesco Maggi

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

Analysis of PDEs 2016-12-06 v3 Metric Geometry

Authors: Giulio Ciraolo , Alessio Figalli , Francesco Maggi

Abstract

We prove a quantitative structure theorem for metrics on $\mathbf{R}^n$ 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 $\mathbf{R}^n$ related to the Yamabe flow.

Keywords

conformal metrics scalar curvature quantitative structure theorem fast diffusion equation Yamabe flow relative entropy

Cite

@article{arxiv.1602.01916,
  title  = {A quantitative analysis of metrics on $\mathbf{R}^n$ with almost constant positive scalar curvature, with applications to fast diffusion flows},
  author = {Giulio Ciraolo and Alessio Figalli and Francesco Maggi},
  journal= {arXiv preprint arXiv:1602.01916},
  year   = {2016}
}

Comments

Because of a gap in one proof in the previous version, we replaced the paper with a weaker version of our Theorem 1.1. Still, this result suffices to obtain the main conclusion in the previous paper, namely a quantitative convergence estimate for a fast diffusion equation related to the Yamabe flow

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

Abstract

Keywords

Cite

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