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 …

[图书][B] Curvature: a variational approach

A Agrachev, D Barilari, L Rizzi - 2018 - ams.org
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 …

Principal symbol calculus on contact manifolds

Y Kordyukov, F Sukochev, D Zanin - Lecture Notes in Mathematics, 2024 - Springer
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 …

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 …

On the essential self-adjointness of singular sub-Laplacians

V Franceschi, D Prandi, L Rizzi - Potential Analysis, 2020 - Springer
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 …

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+ …

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 …

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 …

Chemoenzymatic synthesis and pharmacological characterization of functionalized aspartate analogues as novel excitatory amino acid transporter inhibitors

H Fu, J Zhang, PG Tepper, L Bunch… - Journal of Medicinal …, 2018 - ACS Publications
Aspartate (Asp) derivatives are privileged compounds for investigating the roles governed
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

F Baudoin, B Kim, J Wang - arXiv preprint arXiv:1408.0548, 2014 - arxiv.org
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 …