The paper transfers Euclidean affine isoperimetric and Blaschke-Santaló inequalities to static convex domains in hyperbolic space, with equality exactly for the newly defined hyperbolic ellipsoids.
Blaschke, ¨Uber affine Geometrie I: Isoperimetrische Eigenschaften von Ellipse and Ellipsoid , Ber
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Affine isoperimetric type inequalities for static convex domains in hyperbolic space
The paper transfers Euclidean affine isoperimetric and Blaschke-Santaló inequalities to static convex domains in hyperbolic space, with equality exactly for the newly defined hyperbolic ellipsoids.