Interior, Dimension, and Measure of Algebraic Sums of Planar Sets and Curves
Seminar
Speaker
Karoly Simon, Budapest Technical University
Date
21/05/2017 - 15:00 - 14:00Add to Calendar
2017-05-21 14:00:00
2017-05-21 15:00:00
Interior, Dimension, and Measure of Algebraic Sums of Planar Sets and Curves
Recently considerable attention has been paid to the study of arithmetic sums of two planar sets A+G:={a+g: a in A, g in G}. We focus on the case when G is a piecewise C^2 curve, in particular when G is the unit circle. In this case there is a natural guess what the size (Hausdorff dimension, Lebesgue measure) of A+G should be. We verify it under some simple natural assumptions. We also address the more difficult question: under which condition does the set A+G have non-empty interior?
Colloquium room, Mathematics Dept., building 216
אוניברסיטת בר-אילן - Department of Mathematics
mathoffice@math.biu.ac.il
Asia/Jerusalem
public
Place
Colloquium room, Mathematics Dept., building 216
Abstract
Recently considerable attention has been paid to the study of arithmetic sums of two planar sets A+G:={a+g: a in A, g in G}. We focus on the case when G is a piecewise C^2 curve, in particular when G is the unit circle. In this case there is a natural guess what the size (Hausdorff dimension, Lebesgue measure) of A+G should be. We verify it under some simple natural assumptions. We also address the more difficult question: under which condition does the set A+G have non-empty interior?
Last Updated Date : 14/05/2017
