Minkowski Areas and Valuations

Monika Ludwig

doi:10.4310/jdg/1299766685

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Home > Journals > J. Differential Geom. > Volume 86 > Issue 1 > Article

September 2010 Minkowski Areas and Valuations

Monika Ludwig

J. Differential Geom. 86(1): 133-162 (September 2010). DOI: 10.4310/jdg/1299766685

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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.