Integral Geometry and Valuations by Semyon AleskerIntegral Geometry and Valuations by Semyon Alesker

Integral Geometry and Valuations

bySemyon Alesker, Joseph H.G. FuEditorEduardo Gallego

Paperback | October 31, 2014

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In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, provides an introduction to the theory of convex valuations with emphasis on recent developments. In particular, it presents the new structures on the space of valuations discovered after Alesker's irreducibility theorem. The newly developed theory of valuations on manifolds is also described. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló. The approach is new and based on the notions and tools presented in the first part. This original viewpoint not only enlightens the classical integral geometry of euclidean space, but it also allows the computation of kinematic formulas in other geometries, such as hermitian spaces. The book will appeal to graduate students and interested researchers from related fields including convex, stochastic, and differential geometry.
Title:Integral Geometry and ValuationsFormat:PaperbackDimensions:112 pages, 24 × 16.8 × 0.01 inPublished:October 31, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034808739

ISBN - 13:9783034808736

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Table of Contents

Part I: New Structures on Valuations and Applications.- Translation invariant valuations on convex sets.- Valuations on manifolds.- Part II: Algebraic Integral Geometry.- Classical integral geometry.- Curvature measures and the normal cycle.- Integral geometry of euclidean spaces via Alesker theory.- Valuations and integral geometry on isotropic manifolds.- Hermitian integral geometry.