Uniqueness of Energy Minimizing Maps for Almost All Smooth Boundary Data
Libin Mou · 2007
14.46> ' 2 C (@ - ;N ), there exists at m ost o n e m in im izer o f the en ergy R 2 1 ;2 jr u j d x am o n g fu 2 L ( - ;N ) : u j = ' g. @ - - 2 ; + So in part icular, t he nonuniqueness set Z consist ing of all ' 2 C (@ - ;N ) each of which serves as boundary data of at least t wo dierent energy minimizers is of rst category. 1 ;2 It is well known t hat if u , u 2 L ( - ;N ) are energy minimizers with same boundary 1 2 data, and if N is of nonpositive sect ional curvature and u and