Affine invariant valuations on polytopes

Abstract

A classification of SL$(n)$ invariant valuations on the space of convex polytopes in $R^n$ without any continuity assumptions is established. A corresponding result is obtained on the space of convex polytopes in $R^n$ that contain the origin.

References in corpus (1)

• GL(n) contravariant Minkowski valuations

Cited by in corpus (9)

• Valuations on Convex Functions
• Volume, Polar Volume and Euler Characteristic for Convex Functions
• $\mathrm{SL}(n)$ invariant valuations on super-coercive convex functions
• $\mathrm{SL}(\mathrm{n})$ covariant function-valued valuations
• Valuations on Log-Concave Functions
• Valuations on Convex Bodies and Functions
• Geometric valuation theory
• Affine function valued valuations
• $\mathrm{SL}(n)$ contravariant function-valued valuations on polytopes