TY - THES
T1 - Invariants, volumes and heat kernels in sub-Riemannian geometry
Y1 - 2011
A1 - Davide Barilari
KW - Sub-Riemannian geometry
AB - Sub-Riemannian geometry can be seen as a generalization of Riemannian geometry under non-holonomic constraints. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators (see [32, 57, 70, 92] and references therein) and many problems of geometric measure theory (see for instance [18, 79]). In applications it appears in the study of many mechanical problems (robotics, cars with trailers, etc.) and recently in modern elds of research such as mathematical models of human behaviour, quantum control or motion of self-propulsed micro-organism (see for instance [15, 29, 34])\\r\\nVery recently, it appeared in the eld of cognitive neuroscience to model the\\r\\nfunctional architecture of the area V1 of the primary visual cortex, as proposed by Petitot in [87, 86], and then by Citti and Sarti in [51]. In this context, the sub-Riemannian heat equation has been used as basis to new applications in image reconstruction (see [35]).
PB - SISSA
UR - http://hdl.handle.net/1963/6124
U1 - 6005
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -