Resumen de The Hausdorff dimension of visible sets of planar continua

Toby C. O'Neil

• For a compact set and a point , we define the visible part of from to be the set (Here denotes the closed line segment joining to .) In this paper, we use energies to show that if is a compact connected set of Hausdorff dimension greater than one, then for (Lebesgue) almost every point , the Hausdorff dimension of is strictly less than the Hausdorff dimension of . In fact, for almost every , We also give an estimate of the Hausdorff dimension of those points where the visible set has dimension greater than for some .