A lower bound on area of convex hypersurfaces is established via antipodal displacement, confirming the volume conjecture for convex cases in every dimension.
On theorems of B orsuk-- U lam, K akutani-- Y amabe-- Y ujob\^ o and D yson
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Area and antipodal distance in convex hypersurfaces
A lower bound on area of convex hypersurfaces is established via antipodal displacement, confirming the volume conjecture for convex cases in every dimension.