Analysis and Geometry of Markov Diffusion Operators

摘要: Introduction.- Part I Markov semigroups, basics and examples: 1.Markov semigroups.- 2.Model examples.- 3.General setting.- II Three model functional inequalities: 4.Poincare inequalities.- 5.Logarithmic Sobolev 6.Sobolev III Related functional, isoperimetric transportation 7.Generalized 8.Capacity isoperimetry-type 9.Optimal IV Appendices: A.Semigroups of bounded operators on a Banach space.- B.Elements stochastic calculus.- C.Some basic notions in differential Riemannian geometry.- Notations list symbols.- Bibliography.- Index.