| Grant Agreement | University of Jyvskäylä Press Release |
The Jyväskylä Geometry seminar is on Mondays afternoons
in the Department of Mathematics and Statistics.
The meeting is usually from 14:15 to 16:00 in room MaD 380.
Please, check in advance the calendar below.
Blowups and blowdowns of geodesics in Carnot groups (2018)
We study infinitesimal and asymptotic properties of geodesics (i.e., isometric images of intervals) in Carnot groups equipped with arbitrary sub-Finsler metrics. We show that tangents of geodesics are geodesics in some groups of lower nilpotency step. Namely, every blowup curve of every geodesic in every Carnot group is still a geodesic in the group modulo its last layer. With the same approach, we also show that blowdown curves of geodesics in sub-Riemannian Carnot groups are contained in subgroups of lower rank. This latter result can be extended to rough geodesics.
Restricting open surjections (2018)
We show that any continuous open surjection from a complete metric space to another metric space can be restricted to a surjection for which the domain has the same density character as the target. This improves a recent result of Aron, Jaramillo and Le Donne.
A note on topological dimension, Hausdorff measure, and rectifiability (2018)
The purpose of this note is to record a consequence, for general metric spaces, of a recent result of David Bate. We prove the following fact: Let $X$ be a compact metric space of topological dimension $n$. Suppose that the $n$-dimensional Hausdorff measure of $X$, $H^n(X)$, is finite. Suppose further that the lower $n$-density of the measure $H^n(X)$ is positive, $H^n(X)$-almost everywhere in $X$. Then $X$ contains an $n$-rectifiable subset of positive $H^n(X)$-measure. Moreover, the assumption on the lower density is unnecessary if one uses recently announced results of Csörnyei-Jones.
| See the complete list of papers |