论文标题
在弯曲维度条件下，索博莱夫的不平等
Sobolev's inequality under a curvature-dimension condition
论文作者
论文摘要
在本说明中，我们提供了在RICCI弯曲的均匀下限下Sobolev不平等的新证明。该结果最初是由Ilias在1983年获得的。我们的目标是提出一个非常简短的证据，以回顾著名的不平等现象，并解释我们的方法如何依靠梯度流的解释是简单而强大的。特别是，我们阐明了以前许多作品中使用的计算，从Bidaut-V {é} Ron和V {é} Ron的1991年经典作品开始。
In this note we present a new proof of Sobolev's inequality under a uniform lower bound of the Ricci curvature. This result was initially obtained in 1983 by Ilias. Our goal is to present a very short proof, to give a review of the famous inequality and to explain how our method, relying on a gradient-flow interpretation, is simple and robust. In particular, we elucidate computations used in numerous previous works, starting with Bidaut-V{é}ron and V{é}ron's 1991 classical work.
