发表机构
Universitat Jaume I（豪梅一世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究球面上极小嵌入子流形管状邻域中布朗运动平均退出时间，通过径向移植建立双侧界，发现其随子流形维数增大而发散，随余维数增大而趋于零，并推导体积界与Weyl公式比较。
AI 中文摘要
研究了布朗运动从闭合、极小嵌入的\\(n\\)维子流形在\\((n+m)\\)维球面上的管状邻域中退出的平均时间，通过径向移植建立了双侧界。与\\(n=0\\)或\\(m=1\\)时的已知结果一致，平均退出时间随\\(n\to\infty\\)趋于无穷，随\\(m\to\infty\\)趋于0。同时，推导了此类管状邻域的体积界，并与Weyl管公式进行了比较。
英文摘要
The mean exit time of a Brownian motion from a tube around a closed, minimal embedded \(n\)-dimen\-sional submanifold of the \((n+m)\)-dimen\-sional sphere is studied, establishing two-sided bounds via radial transplant. In accordance with known results when \(n = 0\) or \(m = 1,\) the mean exit time goes to infinity as \(n \to \infty\) and to \(0\) as \(m \to \infty.\) Simultaneously, bounds for the volume of such tubes are derived and compared to Weyl's tube formula.
Comments16 pages
