Federer's mathematical work separates thematically into the periods before and after his watershed 1960 paper Normal and integral currents, co-authored with Fleming. That paper provided the first satisfactory general solution to Plateau's problem — the problem of finding a (k+1)-dimensional least-area surface spanning a given k-dimensional boundary cycle in n-dimensional Euclidean space. Their solution inaugurated a new and fruitful period of research on a large class of geometric variational problems — especially minimal surfaces — via what came to be known as Geometric Measure Theory.
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