# Research articles

My papers by year of preprint release.

**2018**[pdf]

**Extensions with Shrinking Fibers**.

[Dynamical systems][pdf]

**Empirical measures: regularity is a counter-curse to dimensionality**

[Probablity theory]**2017**[pdf]

**An optimal transportation approach to the decay of correlations for non-uniformly expanding maps**, to appear in*Ergodic Theory and Dynamical Systems*.

[Dynamical systems][pdf]

**Mixed sectional-Ricci curvature obstructions on tori**with Stéphane Sabourau, to appear in*Journal of Topology and Analysis*.

[Riemannian geometry][pdf]

**Effective high-temperature estimates for intermittent maps**, to appear in*Ergodic Theory and Dynamical Systems*.

[Dynamical systems][pdf]

**Effective limit theorems for Markov chains with a spectral gap**, to appear in the*Annals of Applied Probability*.

[Probability theory][pdf]

**Effective perturbation theory for linear operators**, to appear in*Journal of Operator Theory*.

[Functional Analysis]**2016**[pdf]

**The linear request problem**,*Proceedings of the American Mathematical Society*146-7 (2018).

[Dynamical systems]**2015**[pdf]

**The calculus of the thermodynamical formalism**joint with Paolo Giulietti, Artur O. Lopes and Diego Marcon Farias, to appear in*Journal of the European Mathematical Society*.

[Dynamical systems][pdf]

**On the asymptotic behavior of minimal surfaces in ℍ**joint with Rafe Mazzeo,^{2}× ℝ*Indiana University Mathematics Journal*66 (2017).

[Riemannian geometry, Symmetric spaces]**2014**[pdf]

**Contraction in the Wasserstein metric for some Markov chains, and applications to the dynamics of expanding maps**joint with Artur O. Lopes and Manuel Stadlbauer,*Nonlinearity*28 (2015).

[Dynamical systems][pdf]

**The Cartan-Hadamard conjecture and the Little Prince**joint with Greg Kuperberg; new expanded and modified version of the preprint “The Little Prince and Weil’s isoperimetric problem” (2012). Revised in 2016. Accepté au*Revista Matemática Iberoamericana*.

[Riemannian geometry, Isoperimetric inequalities][pdf]

**Curvatures and anisometry of maps**,*Communications in Analysis and Geometry*23 (2015).

[Riemannian geometry][pdf]

**A geometric study of Wasserstein spaces: isometric rigidity in negative curvature**, joint with Jérôme Bertrand,*International Mathematical Research Notices*2015.

[Optimal transport, Metric geometry]**2013**[pdf]

**A geometric study of Wasserstein spaces: ultrametrics**,*Mathematika*61 (2015).

[Optimal transport, Metric geometry][pdf]

**Yet another short proof of Bourgain’s distorsion estimate for embedding of trees into uniformly convex Banach spaces**,*Israel Journal of Mathematics*200 (2014).

[Functional analysis][pdf]

**Geometry on the utility space**, joint with François Durand, Fabien Mathieu and Ludovic Noirie,*Algorithmic Decision Theory 2015*,*Lecture Notes in Computer Science*9346 (2015).

[Social choice][pdf]

**Coloring distance graphs: a few answers and many questions**,*Geombinatorics*XXIV (2015).

[Combinatorics, Metric geometry]**2012**[pdf]

**A refinement of Günther’s candle inequality**, joint with Greg Kuperberg,*Asian Journal of Mathematics*19 (2015).

[Riemannian geometry][pdf]

**A geometric study of Wasserstein spaces: an addendum on the boundary**, joint with Jérôme Bertrand, conférence*GIS 2013*,*Lecture Notes in Computer Science*Volume 8085 (2013).

[Optimal transport, Metric geometry]**2011**[pdf]

**A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces**,*Journal of Topology and Analysis*4 (2012).

[Optimal transport, Metric geometry]**2010**[pdf]

**Optimal transport and dynamics of expanding circle maps acting on measures**,*Ergodic Theory and Dynamical Systems*33 (2013). This version includes a corrigendum and an addendum written in 2014, to appear in*ETDS*.

[Dynamical systems, Optimal transport][pdf]

**A geometric study of Wasserstein spaces: Hadamard spaces**, joint with Jérôme Bertrand,*Journal of Topology and Analysis*4 (2012).

[Optimal transport, Metric geometry][pdf]

**Approximation by finitely supported measures**,*ESAIM: Control, Optimisation and Calculus of Variations*18 (2012).

[Optimal transport]**2009**[pdf]

**Sharp quantitative isoperimetric inequalities in the**,*L*^{1}Minkowski plane*Proceedings of the American Mathematical Society*138 (2010).

[Isoperimetric inequalities]**2008**[pdf]

**A geometric study of Wasserstein spaces: Euclidean spaces**,*Annali della Scuola Normale Superiore di Pisa*IX (2010).

[Optimal transport, Metric geometry][pdf]

**Almost homogeneous manifolds with boundary**,*Transactions of the American Mathematical Society*, 361 (2009)

[Lie group actions, Symmetric spaces][pdf]

**The space of closed subgroups of**,**R**^{n}is stratified and simply connected*Journal of Topology*2 (2009).

[Topology, Geometry of groups][pdf]

**The space of closed subgroups of**,**R**^{2}and Seifert invariants*The Graduate Student Mathematical Diary*1 (2016).

[Topology, Geometry of groups][pdf]

**Quelques notions d’espaces stratifiés**,*Séminaire de Théorie Spectrale et Géométrie*26 (2007-2008).

[Topology]**2007**[pdf]

**On Lipschitz compactifications of trees**,*Comptes-rendus de l’Académie des science*, 346 (2008).

[Group actions, Metric geometry]**2006**[pdf]

**Rigidity in CR geometry: the Schoen-Webster theorem**, joint with Vincent Minerbe,*Differential Geometry and its Applications*27 (2009)

[CR geometry, Group actions][pdf]

**Sur les remplissages holomorphes équivariants**,*Annales de l’institut Fourier*57 (2007)

[CR geometry, Group actions]**2005**[pdf]

**Symmetric spaces of higher rank do not admit differentiable compactifications**,*Mathematische Annalen*347 (2010).

[Lie group actions, Symmetric spaces]**2004**[pdf]

**On differentiable compactifications of the hyperbolic space**,*Transformation Groups*11 (2006).

[Lie group actions, Riemannian geometry][pdf]

**On differentiable compactifications of the hyperbolic plane and algebraic actions of SL(2;R) on surfaces**,*Geometriae Dedicata*125 (2007).

[Lie group actions, Riemannian geometry]