论文标题
通过爱因斯坦张量
A characterization of non-collapsed $RCD(K, N)$ spaces via Einstein tensors
论文作者
论文摘要
我们研究了指标扩展的第二个主要术语$ c（n）t^{（n+2）/2} g_t $由热核诱导的固定在紧凑型$ rcd（k，n）$空间上的$ l^2 $。我们证明，当且仅当空间不汇合以将常数乘以参考度量时，就证明了该术语的无差异特性。即使是加权的里曼尼亚歧管，这似乎是新的。此外，一个示例告诉我们，结果不能推广到非碰巧情况。从这个意义上讲，我们的结果很敏锐。
We investigate the second principal term in the expansion of metrics $c(n)t^{(n+2)/2}g_t$ induced by heat kernel embedding into $L^2$ on a compact $RCD(K, N)$ space. We prove that the divergence free property of this term in the weak, asymptotic sense if and only if the space is non-collapsed up to multiplying a constant to the reference measure. This seems new even for weighted Riemannian manifolds. Moreover an example tells us that the result cannot be generalized to the noncompact case. In this sense, our result is sharp.
