GeoMeG: Description

The general goal of the project is to study Lie groups equipped with arbitrary distance functions and to develop an adapted geometric measure theory in the non-Riemannian settings.

The main focus is subRiemannian geometry, together with implications to control systems and nilpotent groups. SubRiemannian spaces, and especially Carnot groups, appear in various areas of mathematics, such as control theory, harmonic and complex analysis, subelliptic PDE's and geometric group theory.

The members of the team master methods coming from geometric measure theory, geometric analysis, and group theory; in particular, analysis on metric spaces and Lie group theory.

| Grant Agreement | University of Jyvskäylä Press Release |

People

Principal Investigator

Enrico Le Donne

| Personal website |

Post-Docs

Thibaut Dumont
Matthew Romney
Francesca Tripaldi

Fares Essebei
Eero Hakavuori
Ville Kivioja
Terhi Moisala

Jyväskylä Geometry Seminar

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.

No seminars are preview for the next weeks.

See all current Seminars | Analysis Seminar |

Past Seminars: 2017 | (older) |

Future Events

18th-22nd February 2019 | Jyväskylä (Finland)
Sub-Riemannian Geometry and Beyond, II
| Website |

 Past Events February/2018 Sub-Riemannian Geometry and Beyond Jyväskylä (Finland)

Recent Papers

We warmly thank the CVGMT Team for the support and
for hosting the following papers at CVGMT server.

 Blowups and blowdowns of geodesics in Carnot groups (2018) E. Hakavuori, E. Le Donne    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) J. Jaramillo, E. Le Donne, T. Rajala   (Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas)    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) G. David, E. Le Donne    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 |

Open Positions

Please, contact the PI if you are interested to do a Ph.D. or a postdoc
in the framework of GeoMeG ERC project.

New positions will be open in the next years.

Prof. Enrico Le Donne

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