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Sub-Riemannian Geometry and Subelliptic PDEs

2003
Ishall discuss the connection between complex Hamiltonian mechanics and sub-Riemannian geometry on the Heisenberg group. Using these geometric concepts I shall describe the subelliptic heat kernel and its small time asymptotics. To extend this work to higher step operators I shall apply some of these concepts to a particular step 3 example.
openaire   +1 more source

Sub-Riemannian Geometry and Optimal Transport

2014
The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is completely self-contained: the linear discussion, containing all the proofs of the stated results, leads the reader step by step from the notion of distribution at the very beginning to the ...
openaire   +2 more sources

Riemannian geometry in thermodynamic fluctuation theory

Reviews of Modern Physics, 1995
George Ruppeiner
exaly  

Riemannian geometry for EEG-based brain-computer interfaces; a primer and a review

Brain-Computer Interfaces, 2017
Marco Congedo   +2 more
exaly  

Existence of isoperimetric regions in contact sub-Riemannian manifolds

Journal of Mathematical Analysis and Applications, 2013
Matteo Galli, Manuel Ritoré
exaly  

Multiclass Brain–Computer Interface Classification by Riemannian Geometry

IEEE Transactions on Biomedical Engineering, 2012
Alexandre Barachant   +2 more
exaly  

Sub-Riemannian structures on 3D lie groups

Journal of Dynamical and Control Systems, 2012
Davide Barilari
exaly  

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