Frederick J. Almgren, Jr.

Frederick Justin Almgren Jr. ( born July 3, 1933, Birmingham, Alabama; † February 5, 1997 in Princeton, New Jersey) was an American mathematician who worked on topology, variational calculus, differential geometry, and minimal surfaces.

Life

Almgren completed in 1955 at Princeton University to study engineering and was a fighter pilot in the U.S. Navy. From 1958, he studied mathematics at Brown University with Herbert Federer, who founded the geometric measure theory at this time with Wendell Fleming. In 1962 he received his doctorate in Federer (The homotopy groups of the integral cycle groups, published in: Topology, Vol.1, 1962, p.257 -299 ) and then was instructor at Princeton University, from 1963 to 1965 at the Institute for Advanced Study ( as well as 1974/75, 1981/82, 1985, 1989 and 1992), from 1965 assistant professor, associate professor in 1968 and as of 1972 professor at Princeton (last: Henry Burchard Fine Professor ). In 1970 he was an exchange scientist at the Steklov Institute in Saint Petersburg. In his bone cancer was diagnosed in 1996, and he died a year later of complications from pneumonia after bone marrow transplantation.

1968 to 1970 he was a Sloan Fellow and Guggenheim Fellow 1974-1975. He was a member of the American Association for the Advancement of Science. He was editor and one of the founders of the journal Experimental Mathematics. In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki (minimal surfaces: tangent cones, singularities and topological types) and 1970 in Nice (Geometric measure theory and elliptic variational problems ).

Almgren was married twice. From his first marriage he had a son and a daughter who were also mathematicians. In his second marriage he was married from 1973 with the mathematician Jean Taylor ( professor at Rutgers University) who earned his doctorate at him. With her he had a daughter.

Work

Almgren was known for his work on geometric analysis, especially the study of minimal surfaces.

In the 1960s, he initiated the study of " Varifolds " as a generalization of orientable surfaces descriptive currents ( Currents ) the geometric measure theory on the non- orientable case ( WK Allard later removed).

In the 1970s, he examined minimal problems ( with edges ) were the problem of the shape of the surfaces of soap bubbles closer than the classical Plateau problem ( by Tibor Rado and Jesse Douglas ) or the formulation at Wendell and Fleming (mass Minimizing integral currents ). In the classical Plateau problem some unphysical assumptions such as self-intersection of surfaces, for example, allowed. Almgren get here existence and Regularitätsbeweise that were developed by Jean Taylor continued. They showed, for example, that their bubble model reproduced the experimental observation that the three surfaces meet in a line and four isolated at one point.

From 1974 he worked on the proof that the dimension of the singular quantities mass -minimizing d -dimensional hypersurfaces have a maximum dimension d-2 and have the d-dimensional measure zero. Its original proof, where he worked for 10 years, was 1700 pages long. He was first published in 2000 ( edited by Jean Taylor and Vladimir Scheffer ).

Almgren was also involved in computer simulations of minimal surfaces and turned about a movie.

In the 1980s, he worked with Jean Taylor on evolution equations of the dynamics of surfaces in differential geometry, building on the ideas for the "mean curvature flow" by Ken Brakke (1975). In particular, they were interested in applications in the modeling of crystal growth.

Writings

• Plateau 's problem: an invitation to Varifold geometry, Benjamin, 1966, reprint AMS 2001
• Jean Taylor: American The geometry of Soap Films and Soap Bubbles, Scientific July 1976
• Selected Works, AMS 1999 ( editor Jean Taylor)
• The theory of Varifolds, Lectures Notes, Princeton 1965
• Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Memoirs AMS 1976