Luca Rizzi

Documents

Publications

	Weyl’s law for singular Riemannian manifolds Yacine Chitour , Dario Prandi , Luca Rizzi Journal de Mathématiques Pures et Appliquées, 2024, 181, pp.113-151. ⟨10.1016/j.matpur.2023.10.004⟩ Journal articles hal-01902740v5
	Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries Luca Rizzi , Giorgio Stefani Journal of Functional Analysis, 2023, 285 (9), pp.110099. ⟨10.1016/j.jfa.2023.110099⟩ Journal articles hal-03921243v1
	Heat content asymptotics for sub-Riemannian manifolds Luca Rizzi , Tommaso Rossi Journal de Mathématiques Pures et Appliquées, 2021, 9 (148), pp.267--307. ⟨10.1016/j.matpur.2020.12.004⟩ Journal articles hal-02563090v1
	Bakry-Émery curvature and model spaces in sub-Riemannian geometry Davide Barilari , Luca Rizzi Mathematische Annalen, 2020, 377 (1-2), pp.435-482. ⟨10.1007/s00208-020-01982-x⟩ Journal articles hal-02163180v1
	Branching geodesics in sub-Riemannian geometry Thomas Mietton , Luca Rizzi Geometric And Functional Analysis, 2020, 30, pp.1139 - 1151. ⟨10.1007/s00039-020-00539-z⟩ Journal articles hal-02493682v2
	Curvature: a variational approach Andrei Agrachev , Davide Barilari , Luca Rizzi Memoirs of the American Mathematical Society, 2019, 256 (1225), ⟨10.1090/memo/1225⟩ Journal articles hal-00838195v1
	An introduction to Sub-Laplacians and their self-adjointness properties Luca Rizzi Oberwolfach Reports, 2019, 16 (4), pp.2911-2950. ⟨10.4171/OWR/2019/47⟩ Journal articles hal-02994095v1
	On the Essential Self-Adjointness of Singular Sub-Laplacians Valentina Franceschi , Dario Prandi , Luca Rizzi Potential Analysis, 2019, 53, pp.89-112. ⟨10.1007/s11118-018-09760-w⟩ Journal articles hal-01981861v1
	Sub-Riemannian interpolation inequalities Davide Barilari , Luca Rizzi Inventiones Mathematicae, 2019, 215 (3), pp.977-1038. ⟨10.1007/s00222-018-0840-y⟩ Journal articles hal-01524541v1
	A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and first Dirichlet eigenvalue of hypoelliptic operators Dario Prandi , Luca Rizzi , Marcello Seri Journal of Differential Geometry, 2019, 111 (2), pp.339-379. ⟨10.4310/jdg/1549422105⟩ Journal articles hal-01221668v3
	Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds Luca Rizzi , Pavel Silveira Journal of the Institute of Mathematics of Jussieu, 2019, 18 (4), pp.783-827. ⟨10.1017/S1474748017000226⟩ Journal articles hal-01221661v1
	Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling Andrei Agrachev , Ugo Boscain , Robert Neel , Luca Rizzi ESAIM: Control, Optimisation and Calculus of Variations, In press, 24 (3), pp.1075-1105. ⟨10.1051/cocv/2017037⟩ Journal articles hal-01259762v1
	Sharp measure contraction property for generalized H-type Carnot groups Davide Barilari , Luca Rizzi Communications in Contemporary Mathematics, 2018, 20 (6), ⟨10.1142/S021919971750081X⟩ Journal articles hal-01468967v2
	Quantum confinement on non-complete Riemannian manifolds Dario Prandi , Marcello Seri , Luca Rizzi Journal of Spectral Theory, 2018, 8 (4), pp.1221-1280. ⟨10.4171/JST/226⟩ Journal articles hal-01362030v2
	A counterexample to gluing theorems for MCP metric measure spaces Luca Rizzi Bulletin of the London Mathematical Society, 2018, 50 (5), pp.781-790. ⟨10.1112/blms.12186⟩ Journal articles hal-01635434v1
	On Jacobi fields and canonical connection in sub-Riemannian geometry Davide Barilari , Luca Rizzi Archivum Mathematicum, 2017, 53 (2), pp.77-92. ⟨10.5817/AM2017-2-77⟩ Journal articles hal-01160902v2
	How many geodesics join two points on a contact sub-Riemannian manifold? Antonio Lerario , Luca Rizzi Journal of Symplectic Geometry, 2017, ⟨10.4310/JSG.2017.v15.n1.a7⟩ Journal articles hal-01096718v1
	On the cut locus of free, step two Carnot groups Luca Rizzi , Ulysse Serres Proceedings of the American Mathematical Society, 2017, 145, pp.5341-5357. ⟨10.1090/proc/13658⟩ Journal articles hal-01377408v2
	Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry Ugo Boscain , Robert Neel , Luca Rizzi Advances in Mathematics, 2017, ⟨10.1016/j.aim.2017.04.024⟩ Journal articles hal-01122735v2
	Measure contraction properties of Carnot groups Luca Rizzi Calculus of Variations and Partial Differential Equations, 2016, ⟨10.1007/s00526-016-1002-y⟩ Journal articles hal-01218376v3
	Sub-Riemannian curvature in contact geometry Andrei Agrachev , Davide Barilari , Luca Rizzi Journal of Geometric Analysis, 2016, ⟨10.1007/s12220-016-9684-0⟩ Journal articles hal-01160901v3
	Comparison theorems for conjugate points in sub-Riemannian geometry D. Barilari , L. Rizzi ESAIM: Control, Optimisation and Calculus of Variations, 2016, 22 (2), ⟨10.1051/cocv/2015013⟩ Journal articles hal-00931840v1
	On conjugate times of LQ optimal control problems Andrei Agrachev , Luca Rizzi , Pavel Silveira Journal of Dynamical and Control Systems, 2014, 21 (4), pp.625-641. ⟨10.1007/s10883-014-9251-6⟩ Journal articles hal-01096715v1
	A Formula for Popp’s Volume in Sub-Riemannian Geometry Davide Barilari , Luca Rizzi Analysis and Geometry in Metric Spaces, 2013, 1, ⟨10.2478/agms-2012-0004⟩ Journal articles hal-00751222v1
	The step-harmonic potential Luca Rizzi , Oliver Piattella , Sergio Cacciatori , Vittorio Gorini American Journal of Physics, 2010, pp.19. ⟨10.1119/1.3379290⟩ Journal articles hal-01122823v1
	Our Peculiar Motion Away from the Local Void R. Brent Tully , Edward J. Shaya , Igor D. Karachentsev , Hélène M. Courtois , Dale D. Kocevski The Astrophysical Journal, 2008, 676, pp.184-205. ⟨10.1086/527428⟩ Journal articles hal-00416760v1

	Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures Davide Barilari , Andrea Mondino , Luca Rizzi 2022 Preprints, Working Papers, ... hal-03856993v1
	Comparison theorems on H-type sub-Riemannian manifolds Fabrice Baudoin , Erlend Grong , Gianmarco Molino , Luca Rizzi 2019 Preprints, Working Papers, ... hal-02282474v1
	H-type foliations Fabrice Baudoin , Erlend Grong , Gianmarco Molino , Luca Rizzi 2018 Preprints, Working Papers, ... hal-01947678v1

	The curvature of optimal control problems with applications to sub-Riemannian geometry Luca Rizzi Differential Geometry [math.DG]. Scuola Internazionale di Studi Superiori Avanzati (SISSA, Trieste, Italy), 2014. English. ⟨NNT : ⟩ Theses tel-01122732v1

	Interpolation inequalities and spectral geometry on sub-Riemannian structures Luca Rizzi Optimization and Control [math.OC]. Université Grenoble - Alpes, 2021 Habilitation à diriger des recherches tel-03282295v1

Luca Rizzi

Publications

Weyl’s law for singular Riemannian manifolds

Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries

Heat content asymptotics for sub-Riemannian manifolds

Bakry-Émery curvature and model spaces in sub-Riemannian geometry

Branching geodesics in sub-Riemannian geometry

Curvature: a variational approach

An introduction to Sub-Laplacians and their self-adjointness properties

On the Essential Self-Adjointness of Singular Sub-Laplacians

Sub-Riemannian interpolation inequalities

A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and first Dirichlet eigenvalue of hypoelliptic operators

Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds

Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling

Sharp measure contraction property for generalized H-type Carnot groups

Quantum confinement on non-complete Riemannian manifolds

A counterexample to gluing theorems for MCP metric measure spaces

On Jacobi fields and canonical connection in sub-Riemannian geometry

How many geodesics join two points on a contact sub-Riemannian manifold?

On the cut locus of free, step two Carnot groups

Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry

Measure contraction properties of Carnot groups

Sub-Riemannian curvature in contact geometry

Comparison theorems for conjugate points in sub-Riemannian geometry

On conjugate times of LQ optimal control problems

A Formula for Popp’s Volume in Sub-Riemannian Geometry

The step-harmonic potential

Our Peculiar Motion Away from the Local Void

Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures

Comparison theorems on H-type sub-Riemannian manifolds

H-type foliations

The curvature of optimal control problems with applications to sub-Riemannian geometry

Interpolation inequalities and spectral geometry on sub-Riemannian structures