title: Liberman's lemma
text: # Liberman's lemma
  
  Liberman's lemma is a theorem used in studying intrinsic geometry of convex surface. It is named after Joseph Liberman.
  
  ## Formulation
  
  If $\gamma$ is a unit-speed minimizing geodesic on the surface of a convex body K in Euclidean space then for any point p ∈ K, the function
  
      $t\mapsto \operatorname {dist} ^{2}\circ \gamma (t)-t^{2}$
  
  is concave.
  
  