Weighted area-minimizing submanifolds with soap-film-like singularities assembled from special Lagrangian pieces

A sufficient condition for a set of calibrated submanifolds to be area-minimizing with multiplicities, also call weighted area-minimizing under diffeomorphisms (WAMD) is stated. We construct some WAMD submanifolds by assembling pieces of special Lagrangian (SL) normal bundles including the one of three surfaces meeting at an angle of 120� along soap-film-like singularities. We also mention a symmetry property of SL submanifolds and Bj�rling type problem for SL normal bundles. � 2010 Science China Press and Springer-Verlag Berlin Heidelberg.