Explore the words cloud of the GeoMeG project. It provides you a very rough idea of what is the project "GeoMeG" about.
The following table provides information about the project.
UNIVERSITA DI PISA
|Coordinator Country||Italy [IT]|
|Total cost||1˙248˙560 €|
|EC max contribution||1˙248˙560 € (100%)|
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
|Duration (year-month-day)||from 2017-08-01 to 2022-07-31|
Take a look of project's partnership.
|1||UNIVERSITA DI PISA||IT (PISA)||coordinator||493˙710.00|
|2||JYVASKYLAN YLIOPISTO||FI (JYVASKYLA)||participant||754˙850.00|
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|
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|
JesÃºs A. Jaramillo, Enrico LeÂ 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, FÃsicas y Naturales. Serie A. MatemÃ¡ticas 113/3||2020-03-05|
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
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|
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|
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|
Enrico Le Donne, Sean Li, Terhi Moisala
Infinite-Dimensional Carnot Groups and GÃ¢teaux Differentiability
published pages: , ISSN: 1050-6926, DOI: 10.1007/s12220-019-00324-x
|The Journal of Geometric Analysis||2020-03-05|
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|
Richard M. Aron, JesÃºs 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|
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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