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Title: Functional and isoperimetric inequalities for probability measures on H-type groups
Author: Kontis, Vasilis
ISNI:       0000 0004 2706 2420
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2011
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We investigate isoperimetric and functional inequalities for probability measures in the sub-elliptic setting and more specifically, on groups of Heisenberg type. The approach we take is based on U-bounds as well as a Laplacian comparison theorem for H-type groups. We derive different forms of functional inequalities (of [Phi]-entropy and F-Sobolev type) and show that they can be equivalently stated as isoperimetric inequalities at the level of sets. Furthermore, we study transportation of measure via Talagrand-type inequalities. The methods used allow us to obtain gradient bounds for the heat semigroup. Finally, we examine some properties of more general operators given in Hormander’s sum of squares form and show that the associated semigroup converges to a probability measure as t → [infinity].
Supervisor: Zegarlinski, Boguslaw Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral