Quantitative rectifiability in Euclidean and non-Euclidean spaces
Main funder
Funder's project number: 343256
Funds granted by main funder (€)
- 171 856,00
Funding program
Project timetable
Project start date: 01/09/2020
Project end date: 31/08/2022
Summary
The 5-year Academy Research Fellowship project "Quantitative rectifiability in Euclidean and non-Euclidean spaces" takes place at the Department of Mathematics and Statistics, University of Jyväskylä, and studies sets with integer dimension. A basic result in geometric measure theory (GMT) says that these sets fall essentially into two classes: rectifiable, and unrectifiable. A large amount of GMT deals with the question: how do analytic and geometric properties of sets from the two classes differ? For example, it is known that rectifiable sets are "visible" and unrectifiable sets are "invisible". The current project continues research in this tradition, attempting to answer some notable open problems. The precise connection between visibility and rectifiability is one of them. Also, the theory of rectifiability will be developed in the Heisenberg group, which is the three-dimensional space equipped with a "non-Euclidean" geometry.
