New structures on valuations and applications
Semyon Alesker
TL;DR
This paper reviews recent advances in valuation theory on convex sets and manifolds, emphasizing applications in integral geometry and discussing various practical applications.
Contribution
It provides a comprehensive overview of recent developments in valuation theory and explores their applications in integral geometry.
Findings
Enhanced understanding of valuation structures on convex sets
New applications of valuations in integral geometry
Connections between valuations and manifold theory
Abstract
An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are discussed.
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Taxonomy
TopicsPoint processes and geometric inequalities · Optimization and Variational Analysis