Opendata, web and dolomites


Geometry of Metric groups

Total Cost €


EC-Contrib. €






 GeoMeG project word cloud

Explore the words cloud of the GeoMeG project. It provides you a very rough idea of what is the project "GeoMeG" about.

harmonic    hausdorff    de    examples    trailers    position    perimeter    differentiation    spaces    truck    graduation    nash    limits    theory    geodesics    group    obtaining    embedding    finland    mathematics    lattice    5th    subelliptic    university    groups    received    curves    permanent    trajectories    park    combination    geometric    rectifiability    international    links    he    distances    yale    structure    net    appear    pi    relation    infinitesimal    grow    kleiner    maps    metric    locally    hilbert    pisa    asymptotic    geometry    orsay    plan    nilpotent    compact    allowed    pde    collaborations    smoothness    volume    gromov    abate    fellow    prove    isometric    carnot    giorgi    plans    corners    isometries    regularity    subriemannian    lie    questions    what    tackle    myers    prestigious    distinguished    finite    steenrod    eth    degree    msri    homogeneous    phd    fast    academy    solutions    sns    asymptotics    movement    advisor    implications    theorem    lipschitz    tangents    techniques    minimality    first   

Project "GeoMeG" data sheet

The following table provides information about the project.


Organization address
city: PISA
postcode: 56126

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Italy [IT]
 Total cost 1˙248˙560 €
 EC max contribution 1˙248˙560 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-08-01   to  2022-07-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITA DI PISA IT (PISA) coordinator 493˙710.00
2    JYVASKYLAN YLIOPISTO FI (JYVASKYLA) participant 754˙850.00


 Project objective

What are the best trajectories to park a truck with several trailers? How fast can a lattice grow? These are some of the questions studied in this project because both the infinitesimal control structure of movement of a truck and the asymptotic geometry of a (nilpotent) lattice are examples of metric groups: Lie groups with homogeneous distances.

The PI plans to study geometric properties of metric groups and their implications to control systems and nilpotent groups. In particular, the plan is to exploit the relation between the regularity of distinguished curves, sets, and maps in subRiemannian groups, volume asymptotics in nilpotent groups, and embedding results. The general goal is to develop an adapted geometric measure theory.

SubRiemannian spaces, and in particular Carnot groups, appear in various areas of mathematics, such as control theory, harmonic and complex analysis, asymptotic geometry, subelliptic PDE's and geometric group theory. The results in this project will provide more links between such areas.

The PI has developed a net of high-level international collaborations and obtained several results via a combination of analysis on metric spaces (differentiation of Lipschitz maps, tangents of measures, and Gromov-Hausdorff limits) and the theory of locally compact groups (Lie group techniques and the solutions of the Hilbert 5th problem). This allowed the PI to solve a number of open problems in the field, such as the analogue of Myers-Steenrod theorem on the smoothness of isometries, the analogue of Nash isometric embedding and the non-minimality of curves with corners. Some of the next aims are to establish an analogue of the De Giorgi's rectifiability result for finite-perimeter sets and prove the smoothness of geodesics, a 30-year-old open problem. The goal of this project is to tackle them, together with many more related questions.

The PI received his first degree at SNS Pisa (advisor: M.Abate) and his PhD from Yale University (advisor: B.Kleiner). Before obtaining a permanent position only three years after graduation, he was at ETH, Orsay, and MSRI. He received the prestigious position of research fellow of the Academy of Finland.


year authors and title journal last update
List of publications.
2020 Eero Hakavuori
Infinite Geodesics and Isometric Embeddings in Carnot Groups of Step 2
published pages: 447-461, ISSN: 0363-0129, DOI: 10.1137/19m1271166
SIAM Journal on Control and Optimization 58/1 2020-04-01
2019 Jesús A. Jaramillo, Enrico Le Donne, Tapio Rajala
Restricting open surjections
published pages: 1795-1798, ISSN: 1578-7303, DOI: 10.1007/s13398-018-0579-8
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113/3 2020-03-05
2020 Luca Capogna, Enrico Le Donne
Conformal equivalence of visual metrics in pseudoconvex domains
published pages: , ISSN: 0025-5831, DOI: 10.1007/s00208-020-01962-1
Mathematische Annalen 2020-03-05
2019 Kai Rajala, Matthew Romney
Reciprocal lower bound on modulus of curve families in metric surfaces
published pages: 681-692, ISSN: 1239-629X, DOI: 10.5186/aasfm.2019.4442
Annales Academiae Scientiarum Fennicae Mathematica 44/2 2020-03-05
2020 Lorenzo Ruffoni, Francesca Tripaldi
Extending an Example by Colding and Minicozzi
published pages: 1028-1041, ISSN: 1050-6926, DOI: 10.1007/s12220-019-00177-4
The Journal of Geometric Analysis 30/1 2020-03-05
2019 Matthew Romney
Singular quasisymmetric mappings in dimensions two and greater
published pages: 479-494, ISSN: 0001-8708, DOI: 10.1016/j.aim.2019.05.022
Advances in Mathematics 351 2020-03-05
2019 Enrico Le Donne, Sean Li, Terhi Moisala
Infinite-Dimensional Carnot Groups and Gâteaux Differentiability
published pages: , ISSN: 1050-6926, DOI: 10.1007/s12220-019-00324-x
The Journal of Geometric Analysis 2020-03-05
2019 Rami Luisto
A Newman property for BLD-mappings
published pages: 135-146, ISSN: 1088-4173, DOI: 10.1090/ecgd/338
Conformal Geometry and Dynamics of the American Mathematical Society 23/8 2020-03-05
2017 Richard M. Aron, Jesús Angel Jaramillo, Enrico Le Donne
Smooth surjections and surjective restrictions
published pages: 525-534, ISSN: 1239-629X, DOI: 10.5186/aasfm.2017.4237
Annales Academiae Scientiarum Fennicae Mathematica 42 2020-03-05
2019 Andrei A. Ardentov, Enrico Le Donne, Yuri L. Sachkov
Sub-Finsler Geodesics on the Cartan Group
published pages: 36-60, ISSN: 1560-3547, DOI: 10.1134/s1560354719010027
Regular and Chaotic Dynamics 24/1 2019-05-15

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