Introduction to the theory of valuations / [edited by] Semyon Alesker

Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: CBMS regional conference series in mathematics ; number 126Publisher: Providence, Rhode Island : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2018Description: 1 Online-RessourceSubject(s): Additional physical formats: 1470443597 | 9781470443597 | 1470447177. | 9781470447175. | Erscheint auch als: No title Druck-Ausgabe | Print version: No title MSC: MSC: *52-02 | 52B45 | 52A39LOC classification:
  • QA166.197
Online resources: Summary: Theory of valuations on convex sets is a classical part of convex geometry which goes back at least to the positive solution of the third Hilbert problem by M. Dehn in 1900. Since then the theory has undergone a multifaceted development. The author discusses some of Hadwiger's results on valuations on convex compact sets that are continuous in the Hausdorff metric. The book also discusses the Klain-Schneider theorem as well as the proof of McMullen's conjecture, which led subsequently to many further applications and advances in the theory. The last section gives an overview of more recent devSummary: 5.2. Klain-Schneider characterization of simple valuations (odd case)Chapter 6. Digression on the theory of generalized functions on manifolds; Chapter 7. The Goodey-Weil imbedding; Chapter 8. Digression on vector bundles; 8.1. Generalized sections of vector bundles and invariant form of the Goodey-Weil imbedding; Chapter 9. The irreducibility theorem; 9.1. The Klain imbedding and the irreducibility theorem in the even case; 9.2. The Schneider imbedding and the irreducibility theorem in the odd case; Chapter 10. Further developments; 10.1. Smooth translation-invariant valuationsSummary: 5.2. Klain-Schneider characterization of simple valuations (odd case)Chapter 6. Digression on the theory of generalized functions on manifolds; Chapter 7. The Goodey-Weil imbedding; Chapter 8. Digression on vector bundles; 8.1. Generalized sections of vector bundles and invariant form of the Goodey-Weil imbedding; Chapter 9. The irreducibility theorem; 9.1. The Klain imbedding and the irreducibility theorem in the even case; 9.2. The Schneider imbedding and the irreducibility theorem in the odd case; Chapter 10. Further developments; 10.1. Smooth translation-invariant valuationsSummary: Theory of valuations on convex sets is a classical part of convex geometry which goes back at least to the positive solution of the third Hilbert problem by M. Dehn in 1900. Since then the theory has undergone a multifaceted development. The author discusses some of Hadwiger's results on valuations on convex compact sets that are continuous in the Hausdorff metric. The book also discusses the Klain-Schneider theorem as well as the proof of McMullen's conjecture, which led subsequently to many further applications and advances in the theory. The last section gives an overview of more recent devPPN: PPN: 1028288786Package identifier: Produktsigel: ZDB-4-NLEBK
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