A lower bound on area of convex hypersurfaces is established via antipodal displacement, confirming the volume conjecture for convex cases in every dimension.
Estimates of volume by the length of shortest closed geodesics on a convex hypersurface
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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.