Herbert Federer
Herbert Federer ( born July 23, 1920 in Vienna, † 21 April 2010) was an American mathematician who worked on geometric measure theory.
Life
Federer emigrated in 1938 to the U.S. and studied mathematics and physics at the University of California, Berkeley, where he received his doctorate in Anthony P. Morse in 1944 (Surface Area). From 1945 he was almost continuously at Brown University. In a work with Wendell Fleming, he gave a more precise formulation of the Plateau problem in the theory of minimal surfaces, which established the field of geometric measure theory. He summarized the research field together in the monograph published in 1969, Geometric Measure Theory.
In 1947, he characterized subsets of the - dimensional Euclidean space which have no measure (not " rectifiable " are ), the fact that they are " invisible" to remain at almost all projections ( examples are fractal sets ). AS Besikowitsch had previously been demonstrated for one-dimensional sets in the plane. Federer examined generally, to what extent can be in geometric investigations steadiness or differentiability replaced by measure-theoretical assumptions, such as Curvature properties in the active Curvature Measures of 1958 ( Transactions of the AMS).
From 1957 to 1960 he was Sloan Fellow and 1975/76 Guggenheim Fellow. Federer was a member of the National Academy of Sciences since 1975. In 1987, he won the Leroy P. Steele with Fleming Prize from the American Mathematical Society ( AMS).
His doctoral include Frederick Almgren (1933-1997) and Robert Hardt.
Writings
- Herbert Federer: Geometric Measure Theory ( = basic teachings of the mathematical sciences with special consideration of the application areas vol 153, ISSN 0072-7830. ). Springer, Berlin and others, 1969 ( ibid. Nachdruck. 1996, ISBN 3-540-60656-4 ).
- Colloquium Lectures on geometric measure theory. In: Bulletin of the American Mathematical Society. Vol 84, 1978, ISSN 0273-0979, pp. 291-338.