6533b7d6fe1ef96bd1265bb0

RESEARCH PRODUCT

A Quantitative Analysis of Metrics on Rn with Almost Constant Positive Scalar Curvature, with Applications to Fast Diffusion Flows

Giulio CiraoloFrancesco MaggiAlessio Figalli

subject

General MathematicsYamabe flow010102 general mathematicsMathematical analysisMetric Geometry (math.MG)01 natural sciencesMathematics - Analysis of PDEsMathematics - Metric Geometry0103 physical sciencesFOS: Mathematics010307 mathematical physics0101 mathematicsDiffusion (business)Constant (mathematics)Quantitative analysis Yamabe flow fast diffusion flowQuantitative analysis (chemistry)Analysis of PDEs (math.AP)MathematicsScalar curvature

description

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.

yearjournalcountryeditionlanguage
2017-05-05
10.1093/imrn/rnx071http://hdl.handle.net/10447/242201