论文标题
对爱因斯坦歧管和应用的估计值
Hitting estimates on Einstein manifolds and applications
论文作者
论文摘要
我们将Benjamini-Pemantle-Peres估计与击中概率和Martin的能力相关的估计值与下面有RICCI曲率的歧管的设置相关。随着我们获得的应用：（1）对布朗尼运动接近ricci-flat流形的高曲率部分的可能性的尖锐估计，（2）证明了纳伯未公开的纳伯定理的证据，即每个不收集的ricci-flat限制ricci-flat的限制是依次的范围，即在两种方程式上的弱点，即在eInstein方程上的较弱的范围（3）有效的跨度（3）有效的互动（3）有效的互动（3）有效的互动（3）有效的互动，有效互动（3） RICCI曲率和正渐近体积比。对于具有双向RICCI边界的歧管和Einstein歧管的歧管，我们还获得了（1）和（2）的概括。
We generalize the Benjamini-Pemantle-Peres estimate relating hitting probability and Martin capacity to the setting of manifolds with Ricci curvature bounded below. As applications we obtain: (1) a sharp estimate for the probability that Brownian motion comes close to the high curvature part of a Ricci-flat manifold, (2) a proof of an unpublished theorem of Naber that every noncollapsed limit of Ricci-flat manifolds is a weak solution of the Einstein equations, (3) an effective intersection estimate for two independent Brownian motions on manifolds with non-negative Ricci curvature and positive asymptotic volume ratio. We also obtain generalizations of (1) and (2) for the manifolds with two-sided Ricci bounds and Einstein manifolds with nonzero Einstein constant.
