@inbook{56811eb554b04d1ca758eec7f20ed20e,
title = "Some Variants of Orponen{\textquoteright}s Theorem on Visible Parts of Fractal Sets",
abstract = "It was recently established by T. Orponen that the visible parts from almost every direction of a compact subset of ℝn have Hausdorff dimension at most n−150n. In this note, we refine Orponen{\textquoteright}s argument in order to show that the visible parts from almost every direction of a compact subset of ℝn have Hausdorff dimension at most n−min\{15,1n+2\}. Moreover, we also show that some classes of dynamically defined Cantor sets K⊂ ℝn with Hausdorff dimension d>max\{3,(n−1)+(n−1)(n+3)2\} have visible parts of Hausdorff dimension at most max\{3d+3d+3,(n+1)d+(n−1)d+2\} from almost every direction.",
author = "Carlos Matheus",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2021",
month = jan,
day = "1",
doi = "10.1007/978-3-030-74863-0\_16",
language = "English",
series = "Lecture Notes in Mathematics",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "517--533",
booktitle = "Lecture Notes in Mathematics",
}