Algebraic structures on valuations, their properties and applications

2003/04/22 by Semyon Alesker
Mathematics · #math.MG #msc:46 #msc:47

paper · pdf

published as Proceedings of the ICM, Beijing 2002, vol. 2, 757--764

arxiv created 2003/04/22 · arxiv updated 2009/11/30

Abstract

We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincaré duality and hard Lefschetz theorem), and their relations and applications to integral geometry.

Related

• New structures on valuations and applications
• Valuations on convex functions and convex sets and Monge-Ampere\n operators
• Non-Archimedean analogue of the space of valuations on convex sets
• Valuations on Banach lattices
• Hard Lefschetz theorem and Hodge-Riemann relations for convex valuations