[For the entire collection see Zbl 0552.00008.]
The author summarizes results given in detail in two other papers [Second fundamental form for varifolds and the existence of surfaces minimising curvature, Indiana Univ. Math. J. 35, 45-71 (1986; Zbl 0561.53008); \(C^{1,\alpha}\) multiple function regularity and tangent cone behaviour for varifolds with p-summable second fundamental form (to appear)]. Some of the proofs are sketched. The author describes the types of varifolds and convergence theorems which he has used in solving the problem of minimizing the curvature of a k-dimensional surface among all k- dimensional surfaces having a given boundary. The author also describes his regularity theorem for k-dimensional varifolds having p-power summable second fundamental form, \(p>k\).