A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries
E Le Donne - Analysis and Geometry in Metric Spaces, 2017 - degruyter.com
Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups
equipped with a path distance that is invariant by left-translations of the group and admit …
equipped with a path distance that is invariant by left-translations of the group and admit …
[图书][B] Curvature: a variational approach
The curvature discussed in this paper is a far reaching generalisation of the Riemannian
sectional curvature. We give a unified definition of curvature which applies to a wide class of …
sectional curvature. We give a unified definition of curvature which applies to a wide class of …
Principal symbol calculus on contact manifolds
Principal Symbol Calculus on Contact Manifolds Page 1 Lecture Notes in Mathematics 2359
Yuri Kordyukov Fedor Sukochev Dmitriy Zanin Principal Symbol Calculus on Contact Manifolds …
Yuri Kordyukov Fedor Sukochev Dmitriy Zanin Principal Symbol Calculus on Contact Manifolds …
Sharp measure contraction property for generalized H-type Carnot groups
D Barilari, L Rizzi - Communications in Contemporary Mathematics, 2018 - World Scientific
We prove that H-type Carnot groups of rank k and dimension n satisfy the MCP (K, N) if and
only if K≤ 0 and N≥ k+ 3 (n− k). The latter integer coincides with the geodesic dimension of …
only if K≤ 0 and N≥ k+ 3 (n− k). The latter integer coincides with the geodesic dimension of …
On the essential self-adjointness of singular sub-Laplacians
We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-
Riemannian manifolds, defined with respect to singular measures. We also show that, in the …
Riemannian manifolds, defined with respect to singular measures. We also show that, in the …
Measure contraction properties of Carnot groups
L Rizzi - Calculus of Variations and Partial Differential …, 2016 - Springer
We prove that any corank 1 Carnot group of dimension k+ 1 k+ 1 equipped with a left-
invariant measure satisfies the MCP (K, N) MCP (K, N) if and only if K ≤ 0 K≤ 0 and N ≥ k+ …
invariant measure satisfies the MCP (K, N) MCP (K, N) if and only if K ≤ 0 K≤ 0 and N ≥ k+ …
Spectral asymptotics for sub-Riemannian Laplacians
YC de Verdiere, L Hillairet, E Trélat - arXiv preprint arXiv:2212.02920, 2022 - arxiv.org
We study spectral properties of sub-Riemannian Laplacians, which are hypoelliptic
operators. The main objective is to obtain quantum ergodicity results, what we have …
operators. The main objective is to obtain quantum ergodicity results, what we have …
Sub-Laplacians on sub-Riemannian manifolds
M Gordina, T Laetsch - Potential Analysis, 2016 - Springer
We consider different sub-Laplacians on a sub-Riemannian manifold M. Namely, we
compare different natural choices for such operators, and give conditions under which they …
compare different natural choices for such operators, and give conditions under which they …
Chemoenzymatic synthesis and pharmacological characterization of functionalized aspartate analogues as novel excitatory amino acid transporter inhibitors
Aspartate (Asp) derivatives are privileged compounds for investigating the roles governed
by excitatory amino acid transporters (EAATs) in glutamatergic neurotransmission. Here, we …
by excitatory amino acid transporters (EAATs) in glutamatergic neurotransmission. Here, we …
Transverse Weitzenb\" ock formulas and curvature dimension inequalities on Riemannian foliations with totally geodesic leaves
We prove a family of new Weitzenb\" ock formulas on a Riemannian foliation with totally
geodesic leaves. These Weitzenb\" ock formulas are naturally parametrized by the canonical …
geodesic leaves. These Weitzenb\" ock formulas are naturally parametrized by the canonical …