Affine Isoperimetric Type Inequalities for Static Convex Domains in Hyperbolic Space (Journal of Mathematical Study, 2025)
In this paper, the notion of hyperbolic ellipsoids in hyperbolic space is introduced. Using a natural orthogonal projection from hyperbolic space to Euclideanspace, we establish affine isoperimetric type inequalities for static convex domains inhyperbolic space. Moreover, equality of such inequalities is characterized by thesehyperbolic ellipsoids.
Keywords: Static convex; Blaschke-Santalό inequality; affine isoperimetric inequality; orthogonal projection; hyperbolic space.