论文标题
$ \ varepsilon $ range在低贝克里 - Émery-ricci曲率范围下的一些功能性不平等
Some functional inequalities under lower Bakry-Émery-Ricci curvature bounds with $\varepsilon$-range
论文作者
论文摘要
对于$ n $维的加权riemannian歧管，$ m $ -bakry-émery-émery-ricci曲率边界带有$ \ varepsilon $ -range，由lu-Minguzzi-ohta引入，集成了恒定的恒定较低界限，并在权重功能方面集成了某些可变范围。在本文中，我们证明了Cheng型不平等和较低$ m $ M $ -Bakry-émery-ricci曲率的本地Sobolev不平等，并带有$ \ varepsilon $ range。这些将$ m \ in（n，\ infty）$ in（ - \ infty，1] \ cup \ {\ infty \} $的$ m \ in（n，\ infty）$ in（n，\ infty）$ m \ in（n，\ infty）$ m \的不等式概括。
For $n$-dimensional weighted Riemannian manifolds, lower $m$-Bakry-Émery-Ricci curvature bounds with $\varepsilon$-range, introduced by Lu-Minguzzi-Ohta, integrate constant lower bounds and certain variable lower bounds in terms of weight functions. In this paper, we prove a Cheng type inequality and a local Sobolev inequality under lower $m$-Bakry-Émery-Ricci curvature bounds with $\varepsilon$-range. These generalize those inequalities under constant curvature bounds for $m \in (n,\infty)$ to $m\in(-\infty,1]\cup\{\infty\}$.
