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.
Ciraolo, G., Figalli, A., Maggi, F. (2017). A Quantitative Analysis of Metrics on Rn with Almost Constant Positive Scalar Curvature, with Applications to Fast Diffusion Flows. INTERNATIONAL MATHEMATICS RESEARCH NOTICES [10.1093/imrn/rnx071].
A Quantitative Analysis of Metrics on Rn with Almost Constant Positive Scalar Curvature, with Applications to Fast Diffusion Flows
CIRAOLO, Giulio;
2017-01-01
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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