科研之友
微信
新浪微博
Facebook
分享链接
摘要
Recently it has been established that for compact sets F lying on a circle S, the harmonic measure in the complement of F with respect to any point a is an element of S \ F has convex density on any arc of F. In this note we give an alternative proof of this fact which is based on random walks, and which also yields an analogue in higher dimensions: for compact sets F lying on a sphere S in R-n, the harmonic measure in the complement of F with respect to any point a is an element of S \ F is subharmonic in the interior of F.
- 出版日期2016-5
