On the convexity of injectivity domains on nonfocal manifolds
  Given a smooth nonfocal compact Riemannian manifold, we show that the so-called Ma--Trudinger--Wang condition implies the convexity of injectivity domains. This improves a previous result by Loeper and Villani. 
Alessio Figalli, Thomas Gallou\"et (INRIA Lille - Nord Europe),   Ludovic Rifford (INRIA Sophia Antipolis, JAD)
math.DG