cam a22 5 4500 558057012 CHVBK 20200914101228.0 m d cr |n |||||||| 190322s2014 sz |||| s 0 0|eng d 978-3-0348-0874-3 978-3-0348-0873-6 (print) 10.1007/978-3-0348-0874-3 doi (SERSOL)ssj0001372669 (IDSBB)006500006 (WaSeSS)ssj0001372669 (OCoLC)893857980 WaSeSS QA639.5-640.7 QA640.7-640.77 QA672 PBMW bicssc PBD bicssc MAT012020 bisacsh MAT008000 bisacsh 516.1 23 516.3/62 23 510 15 Alesker Semyon author Integral Geometry and Valuations [Elektronische Daten] by Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes Basel Springer Basel Imprint: Birkhäuser 2014 1 online resource (VIII, 112 p.) online resource text file PDF rda Advanced Courses in Mathematics - CRM Barcelona 2297-0304 Includes bibliographical references 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. Lizenzbedingungen können den Zugang einschränken. License restrictions may limit access. 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. Mathematics Discrete groups Global differential geometry Integral geometry Graph labelings Graph labelings fast Integral geometry fast Fu Joseph H.G. author Gallego Eduardo editor Solanes Gil editor SpringerLink (Online service) Printed edition 9783034808736 https://link.springer.com/10.1007/978-3-0348-0874-3 Uni Basel: Volltext BK020053 XK020053 XK020000 Springer Mathematics and Statistics eBooks 2014 English/International E-Books von 360MarcUpdates mt SzZuIDS BS/BE IDSBB A100 A100 100FM UBH Kt 22872 NELA1001605 / g/2016/L80115 IDSBB A145 A145 145VT https://link.springer.com/10.1007/978-3-0348-0874-3 IDSBB 100 1- Alesker Semyon author IDSBB 490 1- Advanced Courses in Mathematics - CRM Barcelona 2297-0304 IDSBB 700 1- Fu Joseph H.G. author IDSBB 700 1- Gallego Eduardo editor IDSBB 700 1- Solanes Gil editor IDSBB 710 2- SpringerLink (Online service) IDSBB 776 08 Printed edition 9783034808736 IDSBB 856 40 https://link.springer.com/10.1007/978-3-0348-0874-3 Uni Basel: Volltext IDSBB 100 1- Alesker Semyon 1972- (DE-588)106114187X Verfasser aut IDSBB 490 0- Advanced courses in mathematics CRM Barcelona IDSBB 700 1- Fu Joseph H. G. (DE-588)1061141942 Verfasser aut IDSBB 700 1- Gallego Eduardo Herausgeber edt IDSBB DSV51 DSV01 A100 http://www.ub.unibas.ch/tox/IDSBB/006500006/PDF pdf VIEW Inhaltsverzeichnis ORANGE 364308281 SWISSBIB 364308281