Zobrazeno 1 - 4
of 4
pro vyhledávání: '"27A80, 28A78"'
Autor:
Orponen, Tuomas
This paper contains the following $\delta$-discretised projection theorem for Ahlfors regular sets in the plane. For all $C,\epsilon > 0$ and $s \in [0,1]$, there exists $\kappa > 0$ such that the following holds for all $\delta > 0$ small enough. Le
Externí odkaz:
http://arxiv.org/abs/2410.06872
This expository piece expounds on major themes and clarifies technical details of the paper "Kaufman and Falconer estimates for radial projections and a continuum version of Beck's theorem" of Orponen, Shmerkin, and Wang.
Comment: 35 pages, 2 fi
Comment: 35 pages, 2 fi
Externí odkaz:
http://arxiv.org/abs/2402.11847
Publikováno v:
Geom. Funct. Anal. 34 (2024), no. 1, 164--201
We provide several new answers on the question: how do radial projections distort the dimension of planar sets? Let $X,Y \subset \mathbb{R}^{2}$ be non-empty Borel sets. If $X$ is not contained on any line, we prove that \[ \sup_{x \in X} \dim_{\math
Externí odkaz:
http://arxiv.org/abs/2209.00348
Autor:
Orponen, Tuomas, Shmerkin, Pablo
We prove two new exceptional set estimates for radial projections in the plane. If $K \subset \mathbb{R}^{2}$ is a Borel set with $\dim_{\mathrm{H}} K > 1$, then $$\dim_{\mathrm{H}} \{x \in \mathbb{R}^{2} \, \setminus \, K : \dim_{\mathrm{H}} \pi_{x}
Externí odkaz:
http://arxiv.org/abs/2205.13890