Medial/Skeletal Linking Structures for Multi-Region Configurations

Häftad, Engelska, 2017

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The authors consider a generic configuration of regions, consisting of a collection of distinct compact regions $\{ \Omega_i\}$ in $\mathbb{R}^{n+1}$ which may be either regions with smooth boundaries disjoint from the others or regions which meet on their piecewise smooth boundaries $\mathcal{B}_i$ in a generic way. They introduce a skeletal linking structure for the collection of regions which simultaneously captures the regions' individual shapes and geometric properties as well as the ``positional geometry'' of the collection. The linking structure extends in a minimal way the individual ``skeletal structures'' on each of the regions. This allows the authors to significantly extend the mathematical methods introduced for single regions to the configuration of regions.

Produktinformation

Utgivningsdatum2017-11-01
Mått178 x 254 x undefined mm
Vikt260 g
FormatHäftad
SpråkEngelska
SerieMemoirs of the American Mathematical Society
FörlagAmerican Mathematical Society
ISBN9781470426804

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Matematik inom Naturvetenskap och teknik

IntroductionPart 1. Medial/Skeletal Linking Structures: Multi-region configurations in $\mathbb{R}^{n+1}$Skeletal linking structures for multi-region configurations in ${\mathbb R}^{n+1}$Blum medial linking structure for a generic multi-region configurationRetracting the full Blum medial structure to a skeletal linking structurePart 2. Positional Geometry of Linking Structures: Questions involving positional geometry of a multi-region configurationShape operators and radial flow for a skeletal structureLinking flow and curvature conditionsProperties of regions defined using the linking flowGlobal geometry via medial and skeletal linking integralsPositional geometric properties of multi-region configurationsPart 3. Generic Properties of Linking Structures via Transversality Theorems: Multi-distance and height-distance functions and partial multi-jet spacesGeneric Blum linking properties via transversality theoremsGeneric properties of Blum linking structuresConcluding generic properties of Blum linking structuresPart 4. Proofs and Calculations for the Transversality Theorems: Reductions of the proofs of the transversality theoremsFamilies of perturbations and their infinitesimal propertiesCompleting the proofs of the transversality theoremsAppendix A. List of frequently used notationBibliography.