Valuations on Convex Bodies and Functions
Monika Ludwig, Fabian Mussnig
TL;DR
This paper introduces geometric valuation theory, focusing on classifying valuations on convex bodies and functions that are invariant under specific transformations like SL(n) and rigid motions.
Contribution
It provides new classification results for valuations on convex bodies and functions that are invariant under SL(n) and rigid motions.
Findings
Classification of SL(n) invariant valuations
Classification of rigid motion invariant valuations
Extension of valuation theory to convex functions
Abstract
An introduction to geometric valuation theory is given. The focus is on classification results for invariant and rigid motion invariant valuations on convex bodies and on convex functions.
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Taxonomy
TopicsPoint processes and geometric inequalities