Curvature Measures of Singular Sets (eBook)

Jan Rataj, Martina Zähle (Autoren)

eBook Download: PDF

2019 | 1st ed. 2019
XI, 256 Seiten
Springer International Publishing (Verlag)
978-3-030-18183-3 (ISBN)

Infos

The book describes how curvature measures can be introduced for certain classes of sets with singularities 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 special cases. The measures under consideration form a complete system of certain Euclidean invariants. Techniques of geometric measure theory, in particular, rectifiable currents are applied, and some important integral-geometric formulas are derived. Moreover, an approach to curvatures for a class of fractals is presented, which uses approximation by the rescaled curvature measures of small neighborhoods. The book collects results published during the last few decades in a nearly comprehensive way.

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 Z?hle, 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 Birkh?user and is the author of more than 100 publications (on geometric integration theory, fractal geometry, stochastic geometry, potential analysis, fractional calculus and (s)pde).

Produkt-Details

• Erscheint lt. Verlag: 22.6.2019
• Reihe/Serie: Springer Monographs in Mathematics
• Reihe/Serie: Springer Monographs in Mathematics
• Zusatzinfo: XI, 256 p. 13 illus., 7 illus. in color.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Schlagworte: curvature measure • Gauss-Bonnet Theorem • geometric measure theory • Principal kinematic formula • Steiner formula
• ISBN-10: 3-030-18183-9 / 3030181839
• ISBN-13: 978-3-030-18183-3 / 9783030181833