Citation/Abstract

In this thesis we use the variational method to study minimal laminations and connecting orbits of lattice problem. Our setting is based on discrete variational problem as invested in X. Yang [9]. We prove the lamination structure of non-selfintersecting minimal sets by secondary invariants. With this structure we have another view of results by Yang. We also prove the existence of connecting orbits of two neighboring solutions in the lamination. Our method is based on the barrier functions as introduced in Z. Xia [12].