A sharp exceptional set estimate for visibility

作者：Orponen Tuomas^*

来源：Bulletin of the London Mathematical Society, 2018, 50(1): 1-6.

DOI：10.1112/blms.12103

• 28A75

A Borel set B< subset of>Rn is visible from xRn, if the radial projection of B with base point x has positive Hn-1 measure. I prove that if dimB>n-1, then B is visible from every point xRn\E, where E is an exceptional set with dimension dimE2(n-1)-dimB. This is the sharp bound for all n2. Many parts of the proof were already contained in a recent previous paper by P. Mattila and the author, where a weaker bound for dimE was derived as a corollary from a certain slicing theorem. Here, no improvement to the slicing result is obtained; in brief, the main observation of the present paper is that the proof method gives the optimal result, when applied directly to the visibility problem.

• 出版日期2018-2