Polar duals of rotors
Copyright policy )Polar duals of rotors
Summary: Assume \(K\) is a rotor in a regular simplex of height 1 in an \(n\)-dimensional Euclidean space. Let \(K^*\) denote the polar dual of \(K\). Then the volume \(V(K^*)\) satisfies the inequality \[ V(K^*) \geq (n + 1)^n \omega_n, \] where \(\omega_n\) denotes the volume of an \(n\)-dimensional unit ball. Equality holds if and only if \(K\) is a ball centered at the centroid of the simplex.
volume, regular simplex, Inequalities and extremum problems involving convexity in convex geometry, polar dual, rotor, Convex sets in \(n\) dimensions (including convex hypersurfaces), Length, area, volume and convex sets (aspects of convex geometry)
volume, regular simplex, Inequalities and extremum problems involving convexity in convex geometry, polar dual, rotor, Convex sets in \(n\) dimensions (including convex hypersurfaces), Length, area, volume and convex sets (aspects of convex geometry)
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