Title Integral geometry and valuations / Semyon Alesker, Joseph H.G. Fu ; editors for this volume: Eduardo Gallego, Gil Solanes

Published Basel : Birkhäuser, 2014

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Description 1 online resource (viii, 112 pages) Series Advanced courses in mathematics, CRM Barcelona, 2297-0304 Advanced courses in mathematics, CRM Barcelona, 2297-0304 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 Summary Valuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. 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, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H.G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented in the first part. At the core of this approach lies the close relationship between kinematic formulas and Alesker's product of valuations. This original viewpoint not only enlightens the classical integral geometry of Euclidean space, it has also produced previously unreachable results, such as the explicit computation of kinematic formulas in Hermitian spaces Bibliography Includes bibliographical references Notes Online resource; title from PDF title page (SpringerLink, viewed October 27, 2014) Subject Integral geometry. Graph labelings. Graph labelings Integral geometry Form Electronic book Author Fu, Joseph H. G., author. Gallego, Eduardo, editor. Solanes, Gil, editor ISBN 9783034808743 3034808747 3034808739 9783034808736

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