M. Sharir

activity

20032026

most citedIncidences between points and lines on a two-dimensional variety

158 citations · 543 across the 80 of their papers we have counts for

collaborators

Showing math.MGShow all

3 papers · 1 filter

math.MG2017★ 23 cited

Breaking the 3/2 barrier for unit distances in three dimensions

Joshua Zahl

We prove that every set of $n$ points in $R^{3}$ spans $O (n^{295/197 + ε})$ unit distances. This is an improvement over the previous bound of $O (n^{3/2})$ . A key ingredient in…

math.MG2015★ 6 cited

Distinct distances between points and lines

Micha Sharir, Shakhar Smorodinsky, Claudiu Valculescu +1

We show that for $m$ points and $n$ lines in the real plane, the number of distinct distances between the points and the lines is $Ω (m^{1/5} n^{3/5})$ , as long as $m^{1/2}\le n\le m…

math.MG2014★ 1 cited

On triple intersections of three families of unit circles

Orit E. Raz, Micha Sharir, József Solymosi

Let $p_{1}, p_{2}, p_{3}$ be three distinct points in the plane, and, for $i = 1, 2, 3$ , let $C_{i}$ be a family of $n$ unit circles that pass through $p_{i}$ . We address a conjecture mad…