LEADER 04287nam 22006975 450 001 9910299981603321 005 20200704032523.0 010 $a3-0348-0874-7 024 7 $a10.1007/978-3-0348-0874-3 035 $a(CKB)3710000000269604 035 $a(SSID)ssj0001372669 035 $a(PQKBManifestationID)11787124 035 $a(PQKBTitleCode)TC0001372669 035 $a(PQKBWorkID)11304702 035 $a(PQKB)11405371 035 $a(DE-He213)978-3-0348-0874-3 035 $a(MiAaPQ)EBC6311227 035 $a(MiAaPQ)EBC5587369 035 $a(Au-PeEL)EBL5587369 035 $a(OCoLC)1026458476 035 $a(PPN)182098362 035 $a(EXLCZ)993710000000269604 100 $a20141009d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIntegral Geometry and Valuations /$fby Semyon Alesker, Joseph H.G. Fu ; edited by Eduardo Gallego, Gil Solanes 205 $a1st ed. 2014. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (VIII, 112 p.) 225 1 $aAdvanced Courses in Mathematics - CRM Barcelona,$x2297-0304 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-0348-0873-9 320 $aIncludes bibliographical references. 327 $aPart 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. 330 $aValuations are finitely additive functionals on the space of convex bodies. Their study has become a central subject in convexity theory, with fundamental applications to integral geometry. In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, is devoted to the theory of convex valuations, with emphasis on the latest developments. A special focus is put on the new fundamental structures of the space of valuations discovered after Alesker's irreducibility theorem. Moreover, the author describes the newly developed theory of valuations on manifolds. In the second part, Joseph H. G. Fu gives a modern introduction to integral geometry in the sense of Blaschke and Santaló, based on the notions and tools presented in the first part. At the core of this approach lies the close relationship between kinematic formulas and Alesker's product of valuations. This original viewpoint not only enlightens the classical integral geometry of Euclidean space, it has also produced previously unreachable results, such as the explicit computation of kinematic formulas in Hermitian spaces. 410 0$aAdvanced Courses in Mathematics - CRM Barcelona,$x2297-0304 606 $aConvex geometry 606 $aDiscrete geometry 606 $aGeometry, Differential 606 $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aConvex geometry. 615 0$aDiscrete geometry. 615 0$aGeometry, Differential. 615 14$aConvex and Discrete Geometry. 615 24$aDifferential Geometry. 676 $a516.362 700 $aAlesker$b Semyon$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721673 702 $aFu$b Joseph H.G$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aGallego$b Eduardo$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aSolanes$b Gil$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299981603321 996 $aIntegral Geometry and Valuations$92528334 997 $aUNINA