 Grant Agreement  University of Jyvskäylä Press Release 
Enrico Le Donne
 Personal website 
Daniela Di Donato
Sebastiano Don
Laurent Dufloux
Thibaut Dumont
Rami Luisto
Gabriel Pallier
Francesca Tripaldi
Gioacchino Antonelli
Eero Hakavuori
Ville Kivioja
Terhi Moisala
Alessandro Pilastro
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.
See all current Seminars  Analysis Seminar 
Past Seminars: 2021  2020  2019  2018  2017  (older) 
17^{th}14^{th} April 2030  world wide web
International subRiemannian seminar
 Website 
Past Events  
February/2018  SubRiemannian Geometry and Beyond 
February/2019  SubRiemannian Geometry and Beyond, II 
August/2019  Jyväskylä Summer School  Courses in Geometry 
October/2019  Pansu's Fest, for the 60th birthday of Pierre Pansu 
May/2020  SubRiemannian Geometry and Beyond, III  POSTPONED world wide web 
We warmly thank the CVGMT Team for the support and
for hosting the following papers at CVGMT server.
Nilpotent groups and biLipschitz embeddings into $L^1$ (2022)  
S. ErikssonBique, C. Gartland, E. Le Donne, L. Naples, S. NicolussiGolo 

On rectifiable measures in Carnot groups: MarstrandMattila rectifiability criterion (2022)  
G. Antonelli, A. Merlo (Journal of Functional Analysis) In this paper we continue the study of the notion of $\mathscr{P}$rectifiability in Carnot groups. We say that a Radon measure is $\mathscr{P}_h$rectifiable, for $h\in\mathbb N$, if it has positive $h$lower density and finite $h$upper density almost everywhere, and, at almost every point, it admits a unique tangent measure up to multiples. In this paper we prove a MarstrandMattila rectifiability criterion in arbitrary Carnot groups for $\mathscr{P}$rectifiable measures with tangent planes that admit a normal complementary subgroup. Namely, in this conormal case, even if a priori the tangent planes at a point might not be the same at different scales, a posteriori the measure has a unique tangent almost everywhere. Since every horizontal subgroup of a Carnot group has a normal complement, our criterion applies in the particular case in which the tangents are onedimensional horizontal subgroups. Hence, as an immediate consequence of our MarstrandMattila rectifiability criterion and a result of ChousionisMagnaniTyson, we obtain the onedimensional Preiss's theorem in the first Heisenberg group $\mathbb H^1$. More precisely, we show that a Radon measure $\varphi$ on $\mathbb H^1$ with positive and finite onedensity with respect to the Koranyi distance is absolutely continuous with respect to the onedimensional Hausdorff measure $\mathcal{H}^1$, and it is supported on a onerectifiable set in the sense of Federer, i.e., it is supported on the countable union of the images of Lipschitz maps from $A\subset \mathbb R$ to $\mathbb H^1$. 

Density of the boundary regular set of 2d area minimizing currents with arbitrary codimension and multiplicity (2022)  
S. Nardulli, R. Resende In the present work, we consider area minimizing currents in the general setting of arbitrary codimension and arbitrary boundary multiplicity. We study the boundary regularity of 2d area minimizing currents, beyond that, several results are stated in the more general context of $(C_0,\alpha_0,r_0)$almost area minimizing currents of arbitrary dimension m and arbitrary codimension taking the boundary with arbitrary multiplicity. Furthermore, we do not consider any type of convex barrier assumption on the boundary, in our main regularity result which states that the regular set, which includes onesided and twosided points, of any 2d area minimizing current $T$ is an open dense set in $\Gamma$. 

Local minimizers and Gammaconvergence for nonlocal perimeters in Carnot Groups (2021)  
A. Carbotti, S. Don, D. Pallara, A. Pinamonti (ESAIM cocv) We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in which the De Giorgi's rectifiability Theorem holds, we provide a lower bound for the $\Gamma$liminf of the rescaled energy in terms of the horizontal perimeter. 

Direct limits of infinitedimensional Carnot groups (2021)  
T. Moisala, E. Pasqualetto (Mathematica Scandinavica) We give a construction of direct limits in the category of complete metric scalable groups and provide sufficient conditions for the limit to be an infinitedimensional Carnot group. We also prove a Rademachertype theorem for such limits. 

Lecture notes on subRiemannian geometry from the Lie group viewpoint (2021)  
E. Le Donne These are lecture notes from various courses on subRiemannian geometry. The viewpoint that is emphasised is the one from the Lie group theory and metric geometry. 

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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