Real Analytic and Algebraic Singularities

1. Auflage 1997
ISBN: 978-0-582-32874-7
Verlag: Chapman and Hall/CRC

Buch, Englisch, Band 381, 232 Seiten, Format (B × H): 216 mm x 279 mm, Gewicht: 362 g

Reihe: Chapman & Hall/CRC Research Notes in Mathematics Series

This book contains a collection of papers covering recent progress in a number of areas of singularity theory. Topics include blow analyticity, recent progress in the research on equivalence relations of maps and functions, sufficiency of jets, and the transversality theorem. Geometric and analytic studies of partial differential equations have been developed independently of one another, but the shock wave solutions appearing in natural phenomena are not well understood. Singularity theory may unify these studies and a survey based on this viewpoint is presented in which a new notion of weak solution is introduced. There are also reports on the recent progress in Zariski's conjecture on multiplicities of hypersurfaces, transcendency of analytic sets and on the topology of weighted homogeneous polynomials. This book will be of particular interest to specialists in singularities, partial differential equations, algebraic geometry and control theory.

Autoren/Hrsg.

Fukui, Toshisumi

Izumiya, Shuichi

Koike, Satoshi

Fukuda, Toshisumi

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

ForewardList of participantsTzee-Char Kuo's contributions to real singularitiesBlow-analytic equisingularities, properties, problems and progressOn blow-analytic equivalence of embedded curve singularitiesOn arc-analytic trivialization of singularitiesBlow-analytic retraction onto the central fibreAn example of blow-analytic homeomorphismThe blow analytically constant stratum of real analytic singularitiesSufficiency of jets with respect to L-equivalenceA relative transversality theorem and its applicationsIsomorphism of smooth map germs with isomorphic local algebraQuelques proprietes de la distance geodesiqueRelation between equivalence relations of maps and functionsDuality of the second fundamental formGeometric study of quasilinear first order partial differnetial equationsGeometric approach to blow-up phenomena in non-linear problemsMultiplicity of complex analytic sets and bilipschitz mapstranscendence measures for subsets of local algebrasOn topological invariance of weights for quasihomogeneous polynomialsMultiplicity as a C1 invariant

Über Autor(innen)

Fukui\, Toshisumi; Izumiya\, Shuichi; Koike\, Satoshi; Fukuda\, Toshisumi