The subelliptic heat kernel on SU(2): representations, asymptotics and gradient bounds
By Fabrice Baudoin, Michel Bonnefont. 2008
117 citations recorded by the source corpus.
The Lie group SU(2) endowed with its canonical subriemannian structure appears as a three-dimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic heat kernel on it and some related functional inequalities.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/f159e8c1adb87b9dc2ff68b099e6b3a9ae708684
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In Applied Mathematics
- Davide Barilari
- Fabrice Baudoin
- Nicola Garofalo
- Kazumasa Kuwada
- Michel Bonnefont
- Luigi Ambrosio
- Nicola Gigli
- Andrei A. Agrachev
In Geometry and Topology
- Davide Barilari
- Fabrice Baudoin
- Nicola Garofalo
- Kazumasa Kuwada
- Michel Bonnefont
- Luigi Ambrosio
- Nicola Gigli
- Giuseppe Savar'e
Citations in the corpus
- Log-Sobolev inequalities for subelliptic operators satisfying a generalized curvature dimension inequality (2011, background): “ operator and fails to hold even for simple subelliptic diffusion operators like the sub-Laplacian on the Heisenberg group (see [J]). However in the past few years, numerous works like [BBBC], [BBBQ], [BB], [Bo], [DM], [E], [IKZ], [Li] and [Q] have shown on some examples that the heat semigroup assoc”
- Duality on gradient estimates and Wasserstein controls (2009, background): “sion, see [5, 22] also). • The case q>1 on an arbitrary Lie group [27]. Especially, Kp(t) ≡ Kp for some Kp >0 if it is nilpotent. • The case q>1 with Kq(t) = Kqe−t for some Kq >0 on SU(2) [8]. In all these cases, vis chosen to be a right-invariant Haar measure and hence the associated su”
- Trace heat kernel asymptotics in 3D contact sub-Riemannian geometry (2011, methodology): “Besides these existence results, the geometric meaning of the coefficients in the expansion on the diagonal (and out of that) is far from being understood, even in the simplest 3D case, where the heat kernel has been computed explicitly in some cases of left-invariant structures on Lie groups only (”
- Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries (2011, methodology): “In our approach, we completely avoid those tools from geometry that appear typically Riemannian, and instead base our analysis on a systematic use of some entropic inequalities for the heat semigroup that are inspired by the works [7], [10], [12], and which, as we have stressed above, in the geometr”