TY - JOUR
T1 - Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry
Y1 - 2011
A1 - Andrei A. Agrachev
A1 - Paul Lee
AB - We prove a Bishop volume comparison theorem and a Laplacian comparison\r\ntheorem for three dimensional contact subriemannian manifolds with symmetry.
PB - SISSA
UR - http://hdl.handle.net/1963/6508
N1 - 25 pages
U1 - 6455
U2 - Mathematics
U4 - 1
ER -
TY - JOUR
T1 - Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds
Y1 - 2011
A1 - Andrei A. Agrachev
A1 - Paul Lee
PB - SISSA
UR - http://hdl.handle.net/1963/6507
N1 - This is a revised extended version that contains new results.
U1 - 6454
U2 - Mathematics
U4 - 1
ER -
TY - JOUR
T1 - Continuity of optimal control costs and its application to weak KAM theory
JF - Calculus of Variations and Partial Differential Equations. Volume 39, Issue 1, 2010, Pages 213-232
Y1 - 2010
A1 - Andrei A. Agrachev
A1 - Paul Lee
AB - We prove continuity of certain cost functions arising from optimal control of\\r\\naffine control systems. We give sharp sufficient conditions for this\\r\\ncontinuity. As an application, we prove a version of weak KAM theorem and\\r\\nconsider the Aubry-Mather problems corresponding to these systems.
PB - SISSA
UR - http://hdl.handle.net/1963/6459
N1 - 23 pages, 1 figures
U1 - 6405
U2 - Mathematics
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -
TY - JOUR
T1 - Optimal transportation under nonholonomic constraints
JF - Trans. Amer. Math. Soc. 361 (2009) 6019-6047
Y1 - 2009
A1 - Andrei A. Agrachev
A1 - Paul Lee
AB - We study the Monge\\\'s optimal transportation problem where the cost is given by optimal control cost. We prove the existence and uniqueness of optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures and most importantly the absent of sharp abnormal minimizers. In particular, this result is applicable in the case of subriemannian manifolds with a 2-generating distribution and cost given by d2, where d is the subriemannian distance. Also, we discuss some properties of the optimal plan when abnormal minimizers are present. Finally, we consider some examples of displacement interpolation in the case of Grushin plane.
UR - http://hdl.handle.net/1963/2176
U1 - 2068
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -