Abstract
All continuous $GL(n)$ covariant valuations that map convex bodies to convex bodies are completely classified. This establishes a characterization of moment and projection operators and shows that the Holmes-Thompson area is the unique Minkowski area that is also a bivaluation.
Citation
Monika Ludwig. "Minkowski Areas and Valuations." J. Differential Geom. 86 (1) 133 - 162, September 2010. https://doi.org/10.4310/jdg/1299766685
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