Compact convex sets in 2-dimensional asymmetric normed lattices
  We study the geometric structure of compact convex sets in 2-dimensional asymmetric normed lattices. We prove that every q-compact convex set is strongly q-compact and we give a complete geometric description of the compact convex sets with non empty interior in (R^2, q), where q is an asymmetric lattice norm. 
Natalia Jonard-P\'erez and Enrique A. S\'anchez-P\'erez
math.GN math.FA