10-09-2018
103

数学学院学术报告:Hausdorff dimension, projections and the Kakeya problem

报告人:Pertti Mattila教授(University of Helsinki, Finland)

报告时间:2018年913周四上午10:00-11:00

报告地点:教四4304

报告题目:Hausdorff dimension, projections and the Kakeya problem

报告摘要:Hausdorff dimension is a parameter measuring metric size of general sets. Marstrand proved in 1954 that if A is a Borel set in plane of Hausdorff dimension s, then its almost all projections on lines have dimension s, if s is not greater than 1, and they have positive one-dimensional measure,

if s > 1. I shall discuss some recent developments related to this. A Kakeya (or Besicovitch) set is a set of Lebesgue measure zero containing a unit line segment in every direction. They exist in the Euclidean n-space if n >1, and their Hausdorff dimension is 2 in the plane. It is not known if their Hausdorff dimension is n in every n-space when n > 1. I discuss some relations of this problem to projections.

报告人简介:Pertti Mattila为芬兰赫尔辛基大学教授,国际知名的几何测度论和调和分析专家,ICM45分钟报告人,曾在国际顶级数学期刊“Annals. of Math.”和“Acta Math”发表多篇学术论文,并曾担任“Acta Math”杂志编委。

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