On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds

Baudoin, Fabrice; Gordina, Maria; Mariano, Phanuel

doi:10.1090/proc/14451

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Cited by 3 publications

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“…Note that the Cheng Yau inequality has been proven for all Carnot groups by Baudoin, Gordina and Mariano in [7] by using analytic methods.…”

mentioning

confidence: 99%

Couplings of Brownian Motions on $$SU(2,\mathbb {C})$$

Bénéfice,

Arnaudon,

Bonnefont

2023

Lecture Notes in Computer Science

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In this article we continue the study of couplings of subelliptic Brownian motions on the subRiemannian manifolds SU (2) and SL(2, R). Similar to the case of the Heisenberg group, this subelliptic Brownian motion can be considered as a Brownian motion on the sphere (resp. the hyperbolic plane) together with its swept area modulo 4π. Using this structure, we construct an explicit non co-adapted successful coupling on SU (2) and, under strong conditions on the starting points, on SL(2, R) too. This strategy uses couplings of Brownian bridges, taking inspiration into the work from Banerjee, Gordina and Mariano [3] on the Heisenberg group. We prove that the coupling rate associated to these constructions is exponentially decreasing in time and proportionally to the subRiemannian distance between the starting points. We also give some gradient inequalities that can be deduced from the estimation of this coupling rate.

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“…Note that the Cheng Yau inequality has been proven for all Carnot groups by Baudoin, Gordina and Mariano in [7] by using analytic methods.…”

mentioning

confidence: 99%

Couplings of Brownian Motions on $$SU(2,\mathbb {C})$$

Bénéfice,

Arnaudon,

Bonnefont

2023

Lecture Notes in Computer Science

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Gradient estimate of positive eigenfunctions of sub-Laplacian on complete pseudo-Hermitian manifolds

Ren

2020

Journal of Geometry and Physics

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Couplings of Brownian motions on SU(2) and SL(2,
Bénéfice
2024
Stochastic Processes and their Applications
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0
0
0
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On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds

Abstract: In this note we show how results in [4,6,11] yield the Cheng-Yau estimate on two classes of sub-Riemannian manifolds: Carnot groups and sub-Riemannian manifolds satisfying a generalized curvature-dimension inequality.

Cited by 3 publications

References 25 publications

Couplings of Brownian Motions on $$SU(2,\mathbb {C})$$

Couplings of Brownian Motions on $$SU(2,\mathbb {C})$$

Gradient estimate of positive eigenfunctions of sub-Laplacian on complete pseudo-Hermitian manifolds

Couplings of Brownian motions on SU(2) and SL(2,
Bénéfice
2024
Stochastic Processes and their Applications
0
0
0
0
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On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds

Abstract: In this note we show how results in [4,6,11] yield the Cheng-Yau estimate on two classes of sub-Riemannian manifolds: Carnot groups and sub-Riemannian manifolds satisfying a generalized curvature-dimension inequality.

Cited by 3 publications

References 25 publications

Couplings of Brownian Motions on $$SU(2,\mathbb {C})$$

Couplings of Brownian Motions on $$SU(2,\mathbb {C})$$

Gradient estimate of positive eigenfunctions of sub-Laplacian on complete pseudo-Hermitian manifolds

Couplings of Brownian motions on SU(2) and SL(2,Bénéfice 2024Stochastic Processes and their Applications0000View full textAdd to dashboardCite

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Couplings of Brownian motions on SU(2) and SL(2,
Bénéfice
2024
Stochastic Processes and their Applications
0
0
0
0
View full text Add to dashboard Cite