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New Trends in Sub-Riemannian Geometry

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This volume contains the proceedings of the AMS-EMS-SMF Special Session on Sub-Riemannian Geometry and Interactions, held from July 18-20, 2022, at the Universite de Grenoble-Alpes, Grenoble, France. Sub-Riemannian geometry is a generalization of Riemannian one, where a smooth metric is defined only on a preferred subset of tangent directions. Under the so-called Hormander condition, all points are connected by finite-length curves, giving rise to a well-defined metric space. Sub-Riemannian geometry is nowadays a lively branch of mathematics, connected with probability, harmonic and complex analysis, subelliptic PDEs, geometric measure theory, optimal transport, calculus of variations, and potential analysis. The articles in this volume present some developments of a broad range of topics in sub-Riemannian geometry, including the theory of sub-elliptic operators, holonomy, spectral theory, and the geometry of the exponential map.
Fabrice Baudoin, Aarhus University, Denmark. Luca Rizzi, Scoula Internazionale Superiore di Studi Avanzati, Trieste, Italy.
Articles I. Beschastnyi, Lie groupoids for sub-elliptic operators Samuel Borza, Normal forms for the sub-Riemannian exponential map of $\mathbb {G}_\alpha $, $\operatorname {SU}(2)$, and $\operatorname {SL}(2)$ Fabrice Baudoin and Sylvie Vega-Molino, Holonomy of H-type Foliations Marco Carfagnini and Maria Gordina, Spectral gap bounds on H-type groups Ivan Beschastnyi, Ugo Boscain, Daniele Cannarsa and Eugenio Pozzoli, Embedding the Grushin cylinder in $\mathbf {R}^3$ and Schroedinger evolution Jeremy T. Tyson, Polar coordinates in Carnot groups II Fabrice Baudoin, Michel Bonnefont and Li Chen, Convergence to equilibrium for hypoelliptic non-symmetric Ornstein-Uhlenbeck-type operators Marco Inversi and Giorgio Stefani, Lagrangian stability for a system of non-local continuity equations under Osgood condition
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