Výsledky vyhledávání - "Ludovic Rifford"

Measure contraction properties for two-step analytic sub-Riemannian structures and Lipschitz Carnot groups

Autor: Zeinab Badreddine, Ludovic Rifford

Publikováno v: Annales de l'Institut Fourier
Annales de l'Institut Fourier, 2020, 70 (6)

International audience; We prove that two-step analytic sub-Riemannian structures on a compact analytic manifold equipped with a smooth measure and Lipschitz Carnot groups satisfy measure contraction properties.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::db9ed92d086b4cc9746b7a8fd7f16aa3
https://doi.org/10.5802/aif.3362

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On the stability conjecture for geodesic flows of manifold without conjugate points

Autor: Rafael O. Ruggiero, Ludovic Rifford

Publikováno v: Annales Henri Lebesgue
Annales Henri Lebesgue, 2021, 4, ⟨10.5802/ahl.87⟩

International audience; We study the C 2-structural stability conjecture from Mañé's viewpoint for geodesics flows of compact manifolds without conjugate points. The structural stability conjecture is an open problem in the category of geodesic flo

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2bc130b13ffdcac1939a114beaba4e0f
https://hal.science/hal-01662529

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On the time for a runner to get lonely

Autor: Ludovic Rifford

The Lonely Runner Conjecture asserts that if $n$ runners with distinct constant speeds run on the unit circle $\mathbb{R}/\mathbb{Z}$ starting from $0$ at time $0$, then each runner will at some time $t>0$ be lonely in the sense that she/he will be s

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::aafe56fd31bc87bc7f3ffdf578a6a6be

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Uniquely minimizing costs for the Kantorovitch problem

Autor: Abbas Moameni, Ludovic Rifford

Publikováno v: Annales de la Faculté des Sciences de Toulouse. Mathématiques.
Annales de la Faculté des Sciences de Toulouse. Mathématiques., In press
Annales de la Faculté des Sciences de Toulouse. Mathématiques., Université Paul Sabatier _ Cellule Mathdoc In press

International audience; The purpose of the present paper is to establish comprehensive and systematic sufficient conditions for uniqueness of the Kantorovitch optimizer, an to prove the density of continuous costs on arbitrary manifolds for which opt

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::266201a03a9ef053f205c27287d23644
https://hal.science/hal-01662537

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The Sard conjecture on Martinet surfaces

Autor: André Belotto da Silva, Ludovic Rifford

Publikováno v: Duke Mathematical Journal
Duke Mathematical Journal, Duke University Press, 2018, 167 (8), pp.1433-1471
Duke Math. J. 167, no. 8 (2018), 1433-1471
Duke Mathematical Journal, 2018, 167 (8), pp.1433-1471

Given a totally nonholonomic distribution of rank two on a three-dimensional manifold we investigate the size of the set of points that can be reached by singular horizontal paths starting from a same point. In this setting, the Sard conjecture state

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1105bfd65ee1cb7b2b82cbdddb47e05e
https://hal.archives-ouvertes.fr/hal-01411456/document

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On the Convexity of Injectivity Domains on Nonfocal Manifolds

Autor: Alessio Figalli, Thomas Gallouët, Ludovic Rifford

Publikováno v: SIAM Journal on Mathematical Analysis. 47:969-1000

Given a smooth nonfocal compact Riemannian manifold, we show that the so-called Ma--Trudinger--Wang condition implies the convexity of injectivity domains. This improves a previous result by Loeper and Villani.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a1c06c0529b764094d8be2d5ed6dd0a3
https://doi.org/10.1137/140961821

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Regularity of weak KAM solutions and Mañé’s Conjecture

Autor: Ludovic Rifford

Publikováno v: Séminaire Laurent Schwartz — EDP et applications. :1-22

We provide a crash course in weak KAM theory and review recent results concerning the existence and uniqueness of weak KAM solutions and their link with the so-called Mane conjecture.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a148f8672b808f9ad60f9c0a5d4e2255
https://doi.org/10.5802/slsedp.22

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Ricci curvatures in Carnot groups

Autor: Ludovic Rifford

Publikováno v: Mathematical Control & Related Fields. 3:467-487

We study metric contraction properties for metric spaces associated with left-invariant sub-Riemannian metrics on Carnot groups. We show that ideal sub-Riemannian structures on Carnot groups satisfy such properties and give a lower bound of possible

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f8991c41ec993d00c8e671246f52aa8
https://doi.org/10.3934/mcrf.2013.3.467

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Franks' Lemma for C 2 Mane Perturbations of Riemannian Metrics and Applications to Persistence

Autor: Ludovic Rifford, Rafael O. Ruggiero, Ayadi Lazrag

Publikováno v: Journal of modern dynamics
Journal of modern dynamics, American Institute of Mathematical Sciences, 2016, 10, pp.379-411. ⟨10.3934/jmd.2016.10.379⟩
Journal of modern dynamics, 2016, 10, pp.379-411. ⟨10.3934/jmd.2016.10.379⟩

We prove a uniform Franks' lemma at second order for geodesic flows on a compact Riemannian manifold and apply the result in persistence theory. Our approach, which relies on techniques from geometric control theory, allows us to show that Mane (i.e.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::65382a6ec9576a3453abc577943d235a
https://hal.archives-ouvertes.fr/hal-01111786

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The intrinsic dynamics of optimal transport

Autor: Robert J. McCann, Ludovic Rifford

Publikováno v: Journal de l'École polytechnique — Mathématiques
Journal de l'École polytechnique — Mathématiques, 2016, 3, pp.67-98. ⟨10.5802/jep.29⟩
Journal de l'École polytechnique — Mathématiques, École polytechnique, 2016, 3, pp.67-98. ⟨10.5802/jep.29⟩

The question of which costs admit unique optimizers in the Monge-Kantorovich problem of optimal transportation between arbitrary probability densities is investigated. For smooth costs and densities on compact manifolds, the only known examples for w

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d9aff0bb93c496957a60536bcebb8bf8
https://hal.science/hal-01336327/file/McCannRifford.pdf

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