M. Liero, A. Mielke, G. Savaré:
Optimal transport in competition with reaction: the
  Hellinger-Kantorovich distance and geodesic curves
(preprint) 2015

M. Liero, A. Mielke, G. Savaré:
Optimal Entropy-Transport problems and a new Hellinger-Kantorovich
  distance between positive measures
(preprint) 2015