Frederick Justin Almgren Jr. (July 3, 1933 – February 5, 1997) was an American
mathematician working in
geometric measure theory. He was born in Birmingham, Alabama.
Almgren received a
Guggenheim Fellowship
Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...
in 1974. Between 1963 and 1992 he was a frequent visiting scholar at the
Institute for Advanced Study in Princeton.
Almgren wrote one of the longest papers in mathematics, proving what is now called the
Almgren regularity theorem: the singular set of an ''m''-dimensional mass-minimizing surface has dimension at most ''m−2''. He also developed the concept of
varifold In mathematics, a varifold is, loosely speaking, a measure-theoretic generalization of the concept of a differentiable manifold, by replacing differentiability requirements with those provided by rectifiable sets, while maintaining the general a ...
, first defined by
L. C. Young
Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a British mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He was the son of William Henry ...
in ,
[Young calls these geometric objects ''generalized surfaces'': in his commemorative papers describing the research of Almgren, writes that these are "''essentially the same class of surfaces''".] and proposed them as
generalized solutions to
Plateau's problem in order to deal with the problem even when a concept of
orientation is missing. He played also an important role in the founding of ''
The Geometry Center''.
Almgren was a student of
Herbert Federer, one of the founders of
geometric measure theory, and was the advisor and husband (as his second wife) of
Jean Taylor.
His daughter,
Ann S. Almgren
Ann S. Almgren is an American applied mathematician who works as a senior scientist and group leader of the Center for Computational Sciences and Engineering at the Lawrence Berkeley National Laboratory. Her primary research interests are in comp ...
, is an applied mathematician who works on computational simulations in astrophysics. His son,
Robert F. Almgren, is an applied mathematician working on market microstructure and trade execution.
Almgren died in Princeton, New Jersey on February 5, 1997, aged 63.
Selected publications
*. A set of
mimeographed notes in which Frederick J. Almgren Jr. introduces the term "''varifold''" for the first time.
*. The first widely circulated book describing the concept of a varifold and its applications to the
Plateau's problem.
*.
*.
*. The second edition of the book .
Notes
References
Biographical references
*.
*.
*.
General references
*.
*.
*.
*.
Scientific references
*.
*.
See also
*
Almgren regularity theorem
*
Almgren–Pitts min-max theory
*
Almgren Isomorphism Theorem
External links
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{{DEFAULTSORT:Almgren, Frederick
1933 births
1997 deaths
20th-century American mathematicians
Institute for Advanced Study visiting scholars
Princeton University faculty
Mathematicians from Alabama