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.
Read more about this topic: Herbert Federer
Famous quotes containing the words normal, integral and/or currents:
“The basic thing nobody asks is why do people take drugs of any sort?... Why do we have these accessories to normal living to live? I mean, is there something wrong with society that’s making us so pressurized, that we cannot live without guarding ourselves against it?”
—John Lennon (1940–1980)
“... no one who has not been an integral part of a slaveholding community, can have any idea of its abominations.... even were slavery no curse to its victims, the exercise of arbitrary power works such fearful ruin upon the hearts of slaveholders, that I should feel impelled to labor and pray for its overthrow with my last energies and latest breath.”
—Angelina Grimké (1805–1879)
“For it does not follow because many books are written by persons born in America that there exists an American literature. Books which imitate or represent the thoughts and life of Europe do not constitute an American literature. Before such can exist, an original idea must animate this nation and fresh currents of life must call into life fresh thoughts along its shores.”
—Margaret Fuller (1810–1850)