The Borisenko conjecture is a reverse isoperimetric inequality under a lower curvature constraint. For 
and 
, it asserts that a
lambda-convex lens minimizes volume
among lambda-convex bodies in 
of prescribed surface area.
Such a lens is the intersection of two closed balls of radius
(Drach and Tatarko 2023).
Drach and Tatarko (2026) proved the conjecture in all dimensions, with equality precisely for lenses up to isometry. Their theorem also covers the corresponding constant-curvature
model spaces with the appropriate normal-curvature definition of 
-convexity. The Euclidean theorem holds at fixed surface
area, without fixing the volume.
-Convex
Bodies." 29 Oct 2026.