LEADER 02889nam 22005295 450 001 9910254273503321 005 20220407173345.0 010 $a3-319-57517-1 024 7 $a10.1007/978-3-319-57517-9 035 $a(CKB)3710000001388345 035 $a(DE-He213)978-3-319-57517-9 035 $a(MiAaPQ)EBC4862022 035 $a(PPN)201472929 035 $a(EXLCZ)993710000001388345 100 $a20170517d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMetric diffusion along foliations /$fby Szymon M. Walczak 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XI, 55 p. 19 illus.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 311 $a3-319-57516-3 320 $aIncludes bibliographical references and index. 327 $a1. Wasserstein distance -- 2. Foliations and heat diffusion -- 3. Compact foliations -- 4. Metric diffusion -- 5. Metric diffusion for non-compact foliations. 330 $aUp-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding. Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aTopology 606 $aDifferential geometry 606 $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aTopology. 615 0$aDifferential geometry. 615 14$aTopology. 615 24$aDifferential Geometry. 676 $a516.373 700 $aWalczak$b Szymon M$4aut$4http://id.loc.gov/vocabulary/relators/aut$0766779 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254273503321 996 $aMetric diffusion along foliations$91560482 997 $aUNINA