Geometry, Analysis and Dynamics on sub-Riemannian Manifolds Volume I / [electronic resource] :
Davide Barilari, Ugo Boscain, Mario Sigalotti
- Zuerich, Switzerland : European Mathematical Society Publishing House, 2016
- 1 online resource (332 pages)
- EMS Series of Lectures in Mathematics (ELM) .
Some topics of geometric measure theory in Carnot groups / Hypoelliptic operators and some aspects of analysis and geometry of sub-Riemannian spaces / Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations / Francesco Serra Cassano -- Nicola Garofalo -- Fabrice Baudoin.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
Sub-Riemannian manifolds model media with constrained dynamics: motion at any point is only allowed along a limited set of directions, which are prescribed by the physical problem. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators and degenerate diffusions on manifolds. In the last twenty years, sub-Riemannian geometry has emerged as an independent research domain, with extremely rich motivations and ramifications in several parts of pure and applied mathematics, such as geometric analysis, geometric measure theory, stochastic calculus and evolution equations together with applications in mechanics, optimal control and biology. The aim of the lectures collected here is to present sub-Riemannian structures for the use of both researchers and graduate students.
9783037196625
10.4171/162 doi
Differential & Riemannian geometry
Differential geometry
Partial differential equations
Calculus of variations and optimal control; optimization
Probability theory and stochastic processes
Some topics of geometric measure theory in Carnot groups / Hypoelliptic operators and some aspects of analysis and geometry of sub-Riemannian spaces / Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations / Francesco Serra Cassano -- Nicola Garofalo -- Fabrice Baudoin.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
Sub-Riemannian manifolds model media with constrained dynamics: motion at any point is only allowed along a limited set of directions, which are prescribed by the physical problem. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators and degenerate diffusions on manifolds. In the last twenty years, sub-Riemannian geometry has emerged as an independent research domain, with extremely rich motivations and ramifications in several parts of pure and applied mathematics, such as geometric analysis, geometric measure theory, stochastic calculus and evolution equations together with applications in mechanics, optimal control and biology. The aim of the lectures collected here is to present sub-Riemannian structures for the use of both researchers and graduate students.
9783037196625
10.4171/162 doi
Differential & Riemannian geometry
Differential geometry
Partial differential equations
Calculus of variations and optimal control; optimization
Probability theory and stochastic processes