Abstract
Representations of equiaffine surface area, due to Leichtweiß resp. Schütt & Werner, are generalized top-affine surface area measures. We provide a direct proof which shows that these representations coincide. In addition, we establish two theoremes which in particular characterize all those convex bodies geometrically for which the affine surface area is positive. The present approach also leads to proofs of the equiaffine isoperimetric inequality and the Blaschke-Santaló inequality, including the characterization of the case of equality.
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Hug, D. Contributions to affine surface area. Manuscripta Math 91, 283–301 (1996). https://doi.org/10.1007/BF02567955
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DOI: https://doi.org/10.1007/BF02567955
Key words
- Affine surface area
- affine isoperimetric inequality
- Blaschke-Santaló inequality
- ellipsooids
- generalized Grauß-Kronecker curvature