关于 $\mathbf{R}^n$ 上具有几乎恒定正标量曲率的度量的定量分析，及其在快速扩散流中的应用
偏微分方程分析
2016-12-06 v3 度量几何
摘要
我们证明了 上共形于平坦度量、具有几乎恒定正标量曲率且不能集中多于一个气泡的度量的定量结构定理。作为我们结果的一个应用，我们给出了 中与 Yamabe 流相关的快速扩散方程在相对熵下的定量收敛速率。
引用
@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}
}
备注
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