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.

This project has received funding from the European Research Council (ERC) under the European Union’s ERC Starting Grant (Grant agreement 713998 GeoMeG)

| Grant Agreement | University of Jyvskäylä Press Release |


Principal Investigator

Enrico Le Donne

| Personal website |


Guillaume Buro
Daniela Di Donato
Sebastiano Don
Laurent Dufloux
Thibaut Dumont
Tom Ferragut
Georg Grützner
Rami Luisto
Sam Hagh Shenas Noshari
Gabriel Pallier
Alessandro Socionovo
Francesca Tripaldi

Ph.D. Students

Gioacchino Antonelli
Eero Hakavuori
Ville Kivioja
Denis Marti
Terhi Moisala
Luca Nalon
Nicola Paddeu

Scientific Collaborators and Experts in the Field

See list

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.

Please, check in advance the calendar below.

No seminars are preview for the next weeks.

See all current Seminars | Analysis Seminar |

Past Seminars: 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | (older) |

Recent Papers

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

  Consistency of minimizing movements with smooth mean curvature flow of droplets with prescribed contact-angle in $\mathbb R^3$ (2024)
S. Kholmatov   

In this paper we prove that in $\mathbb R^3$ the minimizing movement solutions for mean curvature motion of droplets, obtained in [Bellettini, Kholmatov: J. Math. Pures Appl. (2018)| ], starting from a regular droplets sitting on the horizontal plane with a regular relative adhesion coefficient, coincide with the smooth mean curvature flow of droplets with a prescribed contact-angle.
  Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions (2024)
F. Almuratov, G. Bellettini, S. Kholmatov   

We study the crystalline curvature flow of planar networks with a single hexagonal anisotropy. After proving the local existence of a classical solution for a rather large class of initial conditions, we classify the homothetically shrinking solutions having one bounded component. We also provide an example of network shrinking to a segment with multiplicity two.
  On the minimality of the Winterbottom shape (2024)
S. Kholmatov   

In this paper we prove that the Winterbottom shape [[Winterbottom: Acta Metallurgica (1967)]] is a volume-constraint minimizer of the corresponding anisotropic capillary functional.
  Minimizing movements for forced anisotropic curvature flow of droplets (2024)
S. Kholmatov   

We study forced anisotropic curvature flow of droplets on an inhomogeneous horizontal hyperplane. As in [[Bellettini, Kholmatov: J. Math. Pures Appl (2018)]] we establish the existence of smooth flow, starting from a regular droplet and satisfying the prescribed anisotropic Young's law, and also the existence of a $1/2$-Hölder continuous in time minimizing movement solution starting from a set of finite perimeter. Furthermore, we investigate various properties of minimizing movements, including comparison principles, uniform boundedness and the consistency with the smooth flow.
  Minimizing movements for the generalized power mean curvature flow (2024)
G. Bellettini, S. Kholmatov   

Motivated by a conjecture of De Giorgi, we consider the Almgren-Taylor-Wang scheme for mean curvature flow, where the volume penalization is replaced by a term of the form \[ \int_{E\Delta F} f\Big(\frac{ {\rm d}_F }{\tau}\Big)~dx \] for $f$ ranging in a large class of strictly increasing continuous functions. In particular, our analysis covers the case \[ f(r) = r^\alpha, \qquad r \geq 0, \quad \alpha>0, \] considered by De Giorgi. We show that the generalized minimizing movement scheme converges to the geometric evolution equation \[ f(v) = - \kappa\quad \text{on $\partial E(t)$,} \] where $\{E(t)\}$ are evolving subsets of $\mathbb{R}^n,$ $v$ is the normal velocity of $\partial E(t),$ and $\kappa$ is the mean curvature of $\partial E(t)$. We extend our analysis to the anisotropic setting, and in the presence of a driving force. We also show that minimizing movements coincide with the smooth classical solution as long as the latter exists. Finally, we prove that in the absence of forcing, mean convexity and convexity are preserved by the weak flow.
  Escape from compact sets of normal curves in Carnot groups (2023)
E. Le Donne, N. Paddeu   

In the setting of subFinsler Carnot groups, we consider curves that satisfy the normal equation coming from the Pontryagin Maximum Principle. We show that, unless it is constant, each such a curve leaves every compact set, quantitatively. Namely, the distance between the points at time 0 and time $t$ grows at least of the order of $t^{1/s}$, where $s$ denotes the step of the Carnot group. In particular, in subFinsler Carnot groups there are no periodic normal geodesics.

| 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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