# Frederick J. Almgren Jr.

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Frederick Justin Almgren
BornJuly 3, 1933
DiedFebruary 5, 1997 (aged 63)
NationalityUnited States
Alma materBrown University
Known forPlateau's problem, theory of varifolds, Almgren–Pitts min-max theory
Spouse(s)Jean Taylor
AwardsGuggenheim Fellowship (1974)
Scientific career
FieldsGeometric measure theory
InstitutionsPrinceton University
Notable students
InfluencedGeometric measure theory

Frederick Justin Almgren Jr. (July 3, 1933, in Birmingham, Alabama – February 5, 1997, in Princeton, New Jersey) was a mathematician working in geometric measure theory.

He received a Guggenheim Fellowship in 1974. Between 1963 and 1992 he was a frequent visiting scholar at the Institute for Advanced Study in Princeton.[1]

He wrote one of the longest papers in mathematics,[2] proving what is now called the Almgren regularity theorem: the singular set of an m-dimensional mass-minimizing hypersurface has dimension at most m−2: he also developed the concept of varifold,[3] first defined by L. C. Young in (Young 1951),[4] 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.

He 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, is an applied mathematician who works on computational simulations in astrophysics.

## Selected publications

• Almgren, Frederick J. Jr. (1964), The theory of varifolds: A variational calculus in the large for the ${\displaystyle k}$-dimensional area integrand, Princeton: Institute for Advanced Study. A set of mimeographed notes in which Frederick J. Almgren Jr. introduces the term "varifold" for the first time.
• Almgren, Frederick J. Jr. (1966), Plateau's Problem: An Invitation to Varifold Geometry, Mathematics Monographs Series (1st ed.), New York–Amsterdam: W. A. Benjamin, Inc., pp. XII+74, MR 0190856, Zbl 0165.13201. The first widely circulated book describing the concept of a varifold and its applications to the Plateau's problem.
• Almgren, Frederick J. Jr. (1999), Taylor, Jean E. (ed.), Selected works of Frederick J. Almgren, Jr., Collected Works, 13, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1067-5, MR 1747253, Zbl 0966.01031.
• Almgren, Frederick J. Jr. (2000), Taylor, Jean E.; Scheffer, Vladimir (eds.), Almgren's big regularity paper. Q-valued functions minimizing Dirichlet's integral and the regularity of area-minimizing rectifiable currents up to codimension 2, World Scientific Monograph Series in Mathematics, 1, River Edge, NJ: World Scientific Publishing Co. Inc., ISBN 978-981-02-4108-7, MR 1777737, Zbl 0985.49001.
• Almgren, Frederick J. Jr. (2001) [1966], Plateau's Problem: An Invitation to Varifold Geometry, Student Mathematical Library, 13 (2nd ed.), Providence, RI: American Mathematical Society, pp. xvi, 78, ISBN 978-0-8218-2747-5, MR 1853442, Zbl 0995.49001. The second edition of the book (Almgren 1966).

## Notes

1. ^ According to Almgren's Community of Scholars web site Profile and to (Mitchell 1980, p. 48): the latter reference lists his appointments at the Institute only up to 1978.
2. ^ Published in book form as (Almgren 2000).
3. ^ See his mimeographed notes (Almgren 1964) and his book (Almgren 1966): the former one is the first exposition of his ideas, but the book (in both its first and second editions (Almgren 2001)) had and still has a wider circulation.
4. ^ Young calls these geometric objects generalized surfaces: in his commemorative papers describing the research of Almgren, Brian White (1997, p.1452, footnote 1, 1998, p.682, footnote 1) writes that these are "essentially the same class of surfaces".