Herbert Federer

Herbert Federer (born July 23, 1920 in Vienna ; † April 21, 2010 ) was an Austrian- American mathematician who dealt with geometric dimension theory.

Life

Federer emigrated to the USA in 1938 and studied mathematics and physics at the University of California, Berkeley , where he received his doctorate in 1944 under Anthony P. Morse ( 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 areas, which founded the field of geometric measurement theory. He summarized the research area in the monograph Geometric Measure Theory published in 1969 .

In 1947 he characterized subsets of the -dimensional Euclidean space that have no measure (not “rectifiable”) by remaining “invisible” in almost all projections (examples are fractal sets). AS Besikowitsch had already proven this for one-dimensional sets in the plane. Federer generally examined the extent to which, in geometrical investigations, requirements for continuity or differentiability can be replaced by assumptions based on dimensions, e.g. B. Curvature properties in 1958 Curvature Measures (Transactions of the AMS). ${\ displaystyle n}$

From 1957 to 1960 he was a Sloan Research Fellow and 1975/76 Guggenheim Fellow . In 1962 he was elected to the American Academy of Arts and Sciences , and since 1975 he has been a member of the National Academy of Sciences . In 1987 he and Fleming won the Leroy P. Steele Prize of the American Mathematical Society (AMS).

His doctoral students include Frederick Almgren (1933–1997) and Robert Hardt .

Fonts

Herbert Federer: Geometric Measure Theory (= basic teachings of the mathematical sciences with special consideration of the areas of application. Vol. 153, ISSN 0072-7830 ). Springer, Berlin et al. 1969 (reprint. Ibid 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.

Web links

Herbert Federer in the Mathematics Genealogy Project (English)
O'Neil on Geometric Measure Theory in the Encyclopaedia of Mathematics
Harold Parks et al. Remembering Herbert Federer (1920–2010). In: Notices of the American Mathematical Society. Vol. 59, No. 5, May 2012, ISSN 1088-9477 , pp. 622-631, (PDF; 900 kB).

Individual evidence

^ Herbert Federer, Wendell H. Fleming: Normal and integral currents. In: Annals of Mathematics . 2nd Series, Vol. 72, No. 3, 1960, pp. 458-520.
↑ The rectifiable subsets of -space. ${\ displaystyle (\ phi, k)}$ ${\ displaystyle n}$ In: Transactions of the American Mathematical Society. Vol. 62, No. 2, 1947, ISSN 0002-9947 , pp. 114-192, online (PDF; 4.35 MB) .

personal data
SURNAME	Federer, Herbert
BRIEF DESCRIPTION	Austrian-American mathematician
DATE OF BIRTH	July 23, 1920
PLACE OF BIRTH	Vienna
DATE OF DEATH	April 21, 2010

[1] Herbert Federer, Wendell H. Fleming: Normal and integral currents. In: Annals of Mathematics . 2nd Series, Vol. 72, No. 3, 1960, pp. 458-520.

[2] The rectifiable subsets of -space. ${\ displaystyle (\ phi, k)}$ ${\ displaystyle n}$ In: Transactions of the American Mathematical Society. Vol. 62, No. 2, 1947, ISSN 0002-9947 , pp. 114-192, online (PDF; 4.35 MB) .