- Background from Geometric Measure Theory. - Background from Convex Geometry. - Background from Differential Geometry and Topology. - Sets with Positive Reach. - Unions of Sets with Positive Reach. - Integral Geometric Formulae. - Approximation of Curvatures. - Characterization Theorems. - Extensions of Curvature Measures to Larger set Classes. - Fractal Versions of Curvatures.
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Jan Rataj, born in 1962 in Prague, studied at Charles University in Prague and defended his PhD at the Mathematical Institute of the Czech Academy of Sciences in 1991. He has been affiliated to Charles University in Prague since 1992, as full professor since 2000. He is the author of approximately 55 publications (on probability theory, stochastic geometry, mathematical analysis, differential and integral geometry).
Martina Zähle, born in1950, obtained her Diploma in 1973 from Moscow State University. She received a PhD in 1978 and Habilitation in 1982 from the Friedrich Schiller University Jena where she has also held the Chair of Probability Theory in 1988, and Geometry in 1991. She has co-edited the proceedings of the international conference series ''Fractal Geometry and Stochastics I -V'', published by Birkhäuser and is the author of more than 100 publications (on geometric integration theory, fractal geometry, stochastic geometry, potential analysis, fractional calculus and (s)pde).
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The book describes how curvature measures can be introduced for certain classes of sets withsingularities in Euclidean spaces. Its focus lies on sets with positive reach and some extensions,which include the classical polyconvex sets and piecewise smooth submanifolds as specialcases. The measures under consideration form a complete system of certain Euclideaninvariants. Techniques of geometric measure theory, in particular, rectifiable currents areapplied, and some important integral-geometric formulas are derived. Moreover, an approach tocurvatures for a class of fractals is presented, which uses approximation by the rescaledcurvature measures of small neighborhoods. The book collects results published during the lastfew decades in a nearly comprehensive way. 268 pp. Englisch. N° de réf. du vendeur 9783030181826
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