论文标题
$ \ text {rcd}^*（k，n）$ space的log-sobolev功能的极端和li-yau估计值
Extremal of Log-Sobolev Functionals and Li-Yau Estimate on $\text{RCD}^*(K,N)$ Spaces
论文作者
论文摘要
In this work, we study the extremal functions of the log-Sobolev functional on compact metric measure spaces satisfying the $\mathrm{RCD}^*(K,N)$ condition for $K$ in $\mathbb{R}$ and $N$ in $(2,\infty)$.我们显示了非负性极端功能的存在，规律性和积极性。基于这些结果，我们证明了li-yau类型的估计值，用于对数sobolev函数的任何非负极函数的对数变换。作为应用程序，我们显示了非负性极端功能的Harnack类型不等式以及上限和上限。
In this work, we study the extremal functions of the log-Sobolev functional on compact metric measure spaces satisfying the $\mathrm{RCD}^*(K,N)$ condition for $K$ in $\mathbb{R}$ and $N$ in $(2,\infty)$. We show the existence, regularity and positivity of non-negative extremal functions. Based on these results, we prove a Li-Yau type estimate for the logarithmic transform of any non-negative extremal functions of the log-Sobolev functional. As applications, we show a Harnack type inequality as well as lower and upper bounds for the non-negative extremal functions.
