SRGI

Sub-Riemannian Geometry and Interactions

Projet ANR SRGI (2015--2021) ANR-15-CE40-0018

Permanent participants:

POLE 1 (SU)	POLE 2 (Inria)	POLE 3 (Toulon)	POLE 4 (Grenoble)
Emmanuel Trélat (coordinator of the project)	Ugo Boscain (coordinator of Pole 2)	Jean-Paul Gauthier (coordinator of Pole 3)	Yves Colin de Verdière (coordinator of Pole 4)
Davide Barilari	Yacine Chitour	Nicolas Boizot	Grégoire Charlot
Roberta Ghezzi	Frédéric Jean	Francesco Rossi	Luca Rizzi
Barbara Gris	Pierre Pansu		Hervé Pajot
Luc Hillairet	Jean Petitot		Constantin Vernicos
Camille Laurent	Dario Prandi
Ludovic Rifford	Mario Sigalotti
Séverine Rigot	Alain Trouvé

Non-permanent participants:
Francesco Boarotto (postdoc ANR, Poles 2 and 3), Valentina Franceschi, Erlend Grong, Mathieu Kohli, Cyril Letrouit, Thomas Mietton, Gabriel Pallier, Sofya Maslovskaya, Tommaso Rossi, Ludovic Sacchelli, Nikhil Savale (postdoc ANR, Poles 1 and 4).

Resume of the project.

Link to the Seminar of Sub-Riemannian Geometry, at Jussieu.

Main events:
- Kick-off day: 2015-11-04 (Paris 6). Schedule.
- Journée "Autour du Laplacien sous-Riemannien", Grenoble, 13 octobre 2016. Affiche. See videos.
- International Conference Geometric Analysis in Control and Vision Theory, Bergen - Voss, Norway, May 2016.
- One-week conference New trends in semiclassical analysis, Chalès (Région Centre, France), December 2016.
- International Conference "Mathematical Control Theory" (with a special session in honor of G. Stefani), Porquerolles, June 2017.
- International Conference "Microlocal analysis, resonances and control theory in PDEs", Sardinia, October 2017.
- Journées sous-Riemanniennes 2017, Grenoble, 17-18 octobre 2017.
- Workshop "Cortical Inspired Non-Holonomic Control for Imaging", Paris, IHP, 28 November 2017. Schedule.
- Conference "Sub-Riemannian Geometry and Beyond", Jyväskylä, Finland, 19--23 February 2018.
- Conference "Sub-Riemannian Geometry and Topolò(gy)", Topolò, Italy, 28-29 juin 2018.
- Journées sous-Riemanniennes 2018, Grenoble, 16-17 octobre 2018.
- Workshop "Cortical models for visual perception and imaging applications", Paris, IMJ, 22 November 2018.
- Conference "Sub-Riemannian Geometry and Beyond. II", Jyväskylä, Finland, 18--22 February 2019.
- Conference "Shape analysis in biology", Paris, 21--22 november 2019.
- Conference "Cortical inspired models for vision and phenomenology of perception", Paris, 23--24 April 2020.
- Final SRGI Conference, Paris, September 7--11 2020.

Publications issued from the project (Hal acronym: SRGI, ref.: ANR-15-CE40-0018):

L. Rifford, Singulières minimisantes en géométrie sous-Riemannienne, Séminaire Bourbaki (2016), no. 1113. Pdf file.
R. Ghezzi, F. Jean, On measures in sub-Riemannian geometry, Séminaire de Théorie Spectrale et Géométrie (Grenoble), 33 (2015-2016), 17--46. Pdf file.
D. Barilari, E. Paoli, Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators, Nonlinear Anal. 164 (2017), 118--134. Pdf file.
U. Boscain, R. Neel, L. Rizzi, Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry, Adv. Math. 314 (2017), 124--184. Pdf file.
N. Savale, Koszul complexes, Birkhoff normal form and the magnetic Dirac operator, Anal. PDE 10 (2017), no. 8, 1793--1844. Pdf file.
N. Juillet, M. Sigalotti, Pliability, or the Whitney extension theorem for curves in Carnot groups, Anal. PDE 10 (2017), no. 7, 1637--1661. Pdf file.
L. Rizzi, U. Serres, On the cut locus of free, step two Carnot groups, Proc. Amer. Math. Soc. 145 (2017), no. 12, 5341--5357. Pdf file.
A. Bohi, D. Prandi, V. Guis, F. Bouchara, J.-P. Gauthier, Fourier descriptors based on the structure of the human primary visual cortex with applications to object recognition, J. Math. Imaging Vision 57 (2017), Issue 1, 117--133. Pdf file.
A. Agrachev, D. Barilari, L. Rizzi, Sub-Riemannian curvature in contact geometry, J. Geom. Anal. 27 (2017), no. 1, 366--408. Pdf file.
D. Barilari, U. Boscain, E. Le Donne, M. Sigalotti, Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions, J. Dynam. Cont. Syst. 23 (2017), 547--575. Pdf file.
D. Barilari, L. Rizzi, On Jacobi fields and canonical connection in sub-Riemannian geometry, Arch. Math. (2017), no. 2, 77--92. Pdf file.
F. Jean, S. Maslovskaya, I. Zelenko, Inverse optimal control problem: the sub-Riemannian case, IFAC-PapersOnLine, 2017, vol. 50, 500--505. Pdf file.
E. Le Donne, S. Rigot, Besicovitch covering property for homogeneous distances on the Heisenberg groups, J. Europ. Math. Soc 19 (2017), no. 5, 1589--1617. Pdf file.
J. Petitot, Elements of Neurogeometry, Functional Architectures of Vision, Lecture Notes in Morphogenesis, Springer, Cham, 2017, 379 pages. Pdf file.
A. Bohi, D. Prandi, V. Guis, F. Bouchara, J.-P. Gauthier, Fourier descriptors based on the structure of the human primary visual cortex with applications to object recognition, J. Math. Imaging Vision 57 (2017), no. 1, 117–133. Pdf file.
Y. Colin de Verdière, L. Hillairet, E. Trélat, Spectral asymptotics for sub-Riemannian Laplacians. I: quantum ergodicity and quantum limits in the 3D contact case, Duke Math. J. 167 (2018), no. 1, 109--174. Pdf file.
D. Barilari, F. Boarotto, On the set of points of smoothness for the value function of affine optimal control problems, SIAM J. Cont. Optim. 56 (2018), no. 2, 649--671. Pdf file.
A. Agrachev, U. Boscain, R. Neel, L. Rizzi, Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling, ESAIM: Cont. Optim. Calc. Var. 24 (2018), no. 3, 1075--1105. Pdf file.
A. Belotto, L. Rifford, The Sard conjecture on Martinet surfaces, Duke Math. J. 167 (2018), no. 8, 1433--1471. Pdf file.
U. Boscain, R. Chertovskih, J.-P. Gauthier, D. Prandi, A. Remizov, Highly corrupted image inpainting through hypoelliptic diffusion, J. Math. Imaging Vision 60 (2018), no. 8, 1231--1245. Pdf file.
E. Grong, P. Pansu, Asymptotic expansions of holonomy, Forum Math. 30 (2018), no. 6, 1363--1385. Pdf file.
D. Barilari, L. Rizzi, Sharp measure contraction property for generalized H-type Carnot groups, Commun. Contemp. Math. 20 (2018), no. 6, 1750081. Pdf file.
N. Savale, A Gutzwiller type trace formula for the magnetic Dirac operator, Geom. Funct. Anal. 28 (2018), no. 5, 1420--1486. Pdf file.
L. Sacchelli, M. Sigalotti, On the Whitney extension property for continuously differentiable horizontal curves in sub-Riemannian manifolds, Calc. Var. Partial Differential Equations 57 (2018), no. 2, Art. 59, 34 pp. Pdf file.
D. Barilari, F. Boarotto, Kolmogorov-Fokker-Planck operators in dimension two: heat kernel and curvature, J. Evol. Eq. 18 (2018), no. 3, 1115--1146. Pdf file.
L. Rizzi, A counterexample to gluing theorems for MCP metric measure space, Bull. London Math. Soc. 50 (2018), no. 5, 781--790. Pdf file.
D. Prandi, J.-P. Gauthier, A semidiscrete version of the Citti-Petitot-Sarti model as a plausible model for anthropomorphic image reconstruction and pattern recognition, SpringerBriefs in Mathematics, BCAM Springer Briefs, 2018, 113 pages. Pdf file.
F. Chittaro, J.-P. Gauthier, Asymptotic ensemble stabilizability of the Bloch equation, Syst. Cont. Letters 113 (2018), 36--44. Pdf file.
U. Boscain, R. Chertovskih, J.-P. Gauthier, D. Prandi, A. Remizov, Cortical-inspired image reconstruction via sub-Riemannian geometry and hypoelliptic diffusion, ESAIM Proc. Surveys 64, EDP Sci., Les Ulis, 2018. Pdf file.
P. Pansu, M. Rumin, On the \ell^{p,q} cohomology of Carnot groups, Ann. H. Lebesgue 1 (2018), 267--295. Pdf file.
H. Pajot, E. Russ, Analyse dans les espaces métriques, Collection "Savoirs actuels", EDP sciences et CNRS Editions (2018), 430 pages.
D. Prandi, L. Rizzi, M. Seri, Quantum confinement on non-complete Riemannian manifolds, J. Spectr. Theory 8 (2018), no. 4, 1221--1280. Pdf file.
F. Boarotto, M. Sigalotti, Time-optimal trajectories of generic control-affine systems at worst iterated Fuller singularities, Ann. Inst. Henri Poincaré Analyse non Lin. 36 (2019), 327--346. Pdf file.
F. Jean, S. Maslovskaya, I. Zelenko, On projective and affine equivalence of sub-Riemannian metrics, Geom. Dedicata 203 (2019), no. 1, 279--319. Pdf file.
V. Franceschi, G. Stefani, Symmetric double bubbles in the Grushin plane, ESAIM Control Optim. Calc. Var. 25 (2019), Art. 77, 37 pp. Pdf file.
D. Barilari, L. Rizzi, Sub-Riemannian interpolation inequalities, Invent. Math. 215 (2019), no. 3, 977--1038. Pdf file.
L. Rizzi, P. Silveira, Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds, J. Inst. Math. Jussieu 18 (2019), no. 4, 783--827. Pdf file.
E. Le Donne, S. Rigot, Besicovitch Covering Property on graded groups and application to measure differentiation, J. Reine Angew. Math. 750 (2019), 241--297. Pdf file.
Y. Chitour, E. Grong, F. Jean, P. Kokkonen, Horizontal holonomy and foliated manifolds, Ann. Inst. Fourier 69 (2019), no. 3, 1047--1086. Pdf file.
A. Agrachev, D. Barilari, E. Paoli, Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics, Ann. Inst. Fourier 69 (2019), no. 3, 1187--1228. Pdf file.
A.-L. Ali, G. Charlot, Local (sub)-Finslerian geometry for the maximum norms in dimension 2, J. Dyn. Control Syst. 25 (2019), no. 3, 457--490. Pdf file.
D. Prandi, L. Rizzi, M. Seri, A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and Dirichlet spectral gap of hypoelliptic operators, J. Differential Geom. 111 (2019), no. 2, 339--379. Pdf file.
D. Barilari, U. Boscain, R. Neel, Heat kernel asymptotics on sR manifolds with symmetries, applications to the bi-Heisenberg group, Ann. Fac. Sci. Toulouse 28 (2019), no. 4, 707--732. Pdf file.
D. Barilari, S. Ivanov, A sub-Riemannian Bonnet-Myers theorem for quaternionic contact structures, Calc. Var. PDE (2019) 58: 37. Pdf file.
U. Boscain, M. Sigalotti, Introduction to controllability of nonlinear systems, in: Contemporary Research in elliptic PDEs and related topics (S. Dipierro, editor), Springer INdAM Series, 2019, 203--219. Pdf file.
F. Jean, S. Maslovskaya, Injectivity of the inverse optimal control problem for control-affine systems, CDC 2019, Nice, 7 pages. Pdf file.
P. Pansu, F. Tripaldi, Averages and the \ell^{q,1} cohomology of Heisenberg groups, Ann. Math. Blaise Pascal 26 (2019), no. 1, 81--100. Pdf file.
F. Boarotto, M. Sigalotti, Dwell-time control sets and applications to the stability analysis of linear switched systems, J. Differential Equations 268 (2020), 1345--1378. Pdf file.
D. Barilari, Y. Chitour, F. Jean, D. Prandi, M. Sigalotti, On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures, J. Math. Pures Appl. 133 (2020), 118--138. Pdf file.
D. Barilari, I. Beschastnyi, A. Lerario, Volume of small balls and sub-Riemannian curvature in 3D contact manifolds, J. Symplectic Geometry 18 (2020), no. 2. Pdf file.
L. Giraldi, F. Jean, Periodical body's deformations are optimal strategies for locomotion, SIAM J. Cont. Optim. 58 (2020), no. 3, 1700--1714. Pdf file.
F. Jean, S. Maslovskaya, I. Zelenko, On Weyl's type theorems and genericity of projective rigidity in sub-Riemannian geometry, Geom. Dedicata (2020). Pdf file.
V. Franceschi, D. Prandi, L. Rizzi, On the essential selfadjointness of sub-Laplacians, Potential Analysis 53 (2020), no. 1, 89--112. Pdf file.
G. Pallier, Sublinear quasiconformality and the large-scale geometry of Heintze groups, Conform. Geom. Dyn. 24 (2020), 131--163. Pdf file.
D. Barilari, L. Rizzi, Bakry-Emery curvature and model spaces sub-Riemannian geometry, Math. Ann. 377 (2020), no. 1-2, 435--482. Pdf file.
A. Baldi, B. Franchi, P. Pansu, L^1-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups, Adv. Math. 366 (2020), 107084, 53 p. Pdf file.
M. Sigalotti, Bounds on time-optimal concatenations of arcs for two-input driftless 3D systems, 21st IFAC World Congress, Jul 2020, Berlin, 6 pages. Pdf file.
T. Mietton, L. Rizzi, Branching geodesics in sub-Riemannian geometry, Geom. Funct. Anal. 30 (2020), no. 4, 1139--1151. Pdf file.
G. Pallier, Large-scale sublinearly Lipschitz geometry of hyperbolic spaces, J. Inst. Math. Jussieu 19 (2020), no. 6, 1831--1876. Pdf file.
F. Boarotto, Y. Chitour, M. Sigalotti, Fuller singularities for generic control-affine systems with an even number of controls, SIAM J. Control Optim. 58 (2020), no. 2, 1207--1228. Pdf file.
O. Oukacha, N. Boizot, Consumption minimization for an academic model of a vehicle, Optimal Control Appl. Methods 41 (2020), no. 4, 1288--1320. Pdf file.
M. Bertalmio, L. Calatroni, V. Franceschi, B. Franceschiello, A. Gomez Villa, D. Prandi, Visual illusions via neural dynamics: Wilson-Cowan-type models and the efficient representation principle, J. Neurophysiology 123 (2020), no. 5, 1606--1618. Pdf file.
L. Rizzi, T. Rossi, Heat content asymptotics for sub-Riemannian manifolds, J. Math. Pures Appl. 148 (2021), 267--307. Pdf file.
J.-P. Gauthier, F. Rossi, A universal gap for non-spin quantum control systems, Proc. Amer. Math. Soc. 149 (2021), no. 3, 1203--1214. Pdf file.
A. Ajami, J.-P. Gauthier, L. Sachelli, Dynamic output stabilization of control systems: unobservable kinematic drone model, Automatica J. IFAC 125 (2021), 109383, 5p. Pdf file.
H. Bahouri, D. Barilari, I. Gallagher, Strichartz estimates and Fourier restriction theorems on the Heisenberg group, J. Fourier Anal. Appl. 27 (2021), no. 2, 21. Pdf file.
A.-L. Ali, G. Charlot, Local contact sub-Finslerian geometry for maximum norms in dimension 3, Math. Cont. Relat. Fields 11 (2021), no. 2, 373--401. Pdf file.
N. Boizot, L. Sacchelli, A bisector line field approach to interpolation of orientation fields, J. Math. Imaging Vision 63 (2021), no. 1, 18--29. Pdf file.
Bertalmio, L. Calatroni, V. Franceschi, B. Franceschiello, D. Prandi, Cortical-inspired Wilson-Cowan-type equations for orientation-dependent contrast perception modelling, J. Math. Imaging Vision 63 (2021), 263--281. Pdf file.
V. Franceschi, D. Prandi, Hardy-type inequalities for the Carnot-Carathéodory distance in the Heisenberg group, J. Geom. Anal. 31 (2021), 2455--2480. Pdf file.
A. Baldi, B. Franchi, P. Pansu, Poincaré and Sobolev inequalities for differential forms in Heisenberg groups, to appear in J. Inst. Math. Jussieu (2021), Preprint hal-01628688 (2017), 28 pages. Pdf file.
T. Rossi, Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group, to appear in Adv. Calc. Var. (2021), Preprint Hal-02960528 (2020), 12 pages. Pdf file.
P. Pansu, Large scale conformal maps, to appear in Ann. Sci. Ec. Norm. Sup. (2021), Preprint Hal-01297830 (2016), 77 pages. Pdf file.
R. Adami, U. Boscain, V. Franceschi, D. Prandi, Point interactions for 3D sub-Laplacians, to appear in Ann. Henri Poincaré Anal. Non Lin., Preprint Hal-02020844 (2019), 22 pages. Pdf file.
C. Laurent, M. Léautaud, Logarithmic decay for damped hypoelliptic wave and Schrödinger equations, to appear in SIAM J. Control Optim. (2021), PrePrint ArXiv:2006.05122 (2020), 17 pages. Pdf file.
Y. Colin de Verdière, L. Hillairet, E. Trélat, Small-time asymptotics of hypoelliptic heat kernels near the diagonal, nilpotentization and related results, to appear in Ann. Henri Lebesgue (2021), Preprint hal-02535865 (2020), 64 pages. Pdf file.
D. Prandi, J.-P. Gauthier, Generalized Fourier-Bessel operator and almost-periodic interpolation and approximation, Preprint arXiv:1612.00056 (2016), 15 pages. Pdf file.
P. Pansu, Cup-products in L^{q,p}-cohomology: discretization and quasi-isometry invariance, Preprint hal-01467860 (2017), 34 pages. Pdf file.
C. Laurent, M. Léautaud, Tunneling estimates and approximate controllability for hypoelliptic equations, PrePrint ArXiv:1703.10797 (2017), 63 pages, to appear in Memoirs AMS. Pdf file.
A. Belotto, A. Figalli, A. Parusinski, L. Rifford, Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3, Preprint ArXiv:1810.03347 (2018), 37 pages. Pdf file.
F. Baudoin, E. Grong, G. Molino, L. Rizzi, H-type foliations, Preprint ArXiv:1812.02563 (2018), 25 pages. Pdf file.
Y. Chitour, D. Prandi, L. Rizzi, Weyl's law for singular Riemannian manifolds, Preprint hal-01902740 (2019), 43 pages. Pdf file.
F. Baudoin, E. Grong, G. Molino, L. Rizzi, Comparison theorems on H-type sub-Riemannian manifolds, Preprint ArXiv:1909.03532 (2019), 44 pages. Pdf file.
D. Barilari, M. Kohli, On sub-Riemannian geodesic curvature in dimension three, Preprint ArXiv-1910.13132 (2019), 26 pages. Pdf file.
C. Letrouit, Subelliptic waves are never observable, Preprint hal-02466229 (2020), 26 pages. Pdf file.
C. Letrouit, Quantum limits of sub-Laplacians via joint spectral calculus, Preprint hal-02886099 (2020), 35 pages. Pdf file.
C. Fermanian Kammemer, C. Letrouit, Observability and controllability for the Schrödinger equation on quotients of groups of Heisenberg type, Preprint hal-02951662 (2020), 42 pages. Pdf file.
C. Letrouit, C. Sun, Observability of Baouendi-Grushin-type equations through resolvent estimates, Preprint hal-02964024 (2020), 37 pages. Pdf file.
V. Franceschi, R. Monti, A. Righini, M. Sigalotti, The isoperimetric problem for regular and crystalline norms in H1, Preprint hal-02905108 (2020), 42 pages. Pdf file.
A. Baldi, B. Franchi, P. Pansu, Cohomology of annuli, duality and L^\infty-differential forms on Heisenberg groups, Preprint hal-03157163 (2021), 35 pages. Pdf file.
C. Llosa Isenrich, G. Pallier, R. Tessera, Cone-equivalent nilpotent groups with different Dehn functions, Preprint ArXiv:2008.01211 (2021), 64 pages. Pdf file.