We prove a quantitative structure theorem for metrics on 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 R^n related to the Yamabe flow.
A Quantitative Analysis of Metrics on R-n with Almost Constant Positive Scalar Curvature, with Applications to Fast Diffusion Flows / G. Ciraolo, A. Figalli, F. Maggi. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - :21(2018), pp. rnx071.6780-rnx071.6797.
A Quantitative Analysis of Metrics on R-n with Almost Constant Positive Scalar Curvature, with Applications to Fast Diffusion Flows
G. Ciraolo;
2018
Abstract
We prove a quantitative structure theorem for metrics on 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 R^n related to the Yamabe flow.
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