Frank Morgan is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and the Webster Atwell '21 Professor of Mathematics, Emeritus, at

Williams College Williams College is a private liberal arts college in Williamstown, Massachusetts. It was established as a men's college in 1793 with funds from the estate of Ephraim Williams, a colonist from the Province of Massachusetts Bay who was kille ...

. He is known for contributions to

geometric measure theory In mathematics, geometric measure theory (GMT) is the study of geometric properties of sets (typically in Euclidean space) through measure theory. It allows mathematicians to extend tools from differential geometry to a much larger class of ...

minimal surface In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below). The term "minimal surface" is used because these surfaces originally arose as surfaces tha ...

s, and differential geometry, including the resolution of the

double bubble conjecture In the mathematical theory of minimal surfaces, the double bubble theorem states that the shape that encloses and separates two given volumes and has the minimum possible surface area is a ''standard double bubble'': three spherical surfaces meet ...

. He was vice-president of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

and the Mathematical Association of America. Morgan studied at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern t ...

and

Princeton University Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the n ...

, and received his Ph.D. from Princeton in 1977, under the supervision of

Frederick J. Almgren Jr. 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 in 1974. Between 1963 and 1992 he ...

He taught at MIT for ten years before joining the Williams faculty. Morgan is the founder of SMALL, one of the largest and best known summer undergraduate Mathematics research programs. In 2012 he became a fellow of the

. Frank Morgan is also an avid dancer. He gained temporary fame for his work "Dancing the Parkway".

Mathematical work

He is known for proving, in collaboration with Michael Hutchings, Manuel Ritoré, and Antonio Ros, the

Double Bubble conjecture In the mathematical theory of minimal surfaces, the double bubble theorem states that the shape that encloses and separates two given volumes and has the minimum possible surface area is a ''standard double bubble'': three spherical surfaces meet ...

, which states that the minimum-surface-area enclosure of two given volumes is formed by three spherical patches meeting at 120-degree angles at a common circle. He has also made contributions to the study of manifolds with density, which are

Riemannian manifold In differential geometry, a Riemannian manifold or Riemannian space , so called after the German mathematician Bernhard Riemann, is a real, smooth manifold ''M'' equipped with a positive-definite inner product ''g'p'' on the tangent spac ...

s together with a measure of volume which is deformed from the standard Riemannian volume form. Such deformed volume measures suggest modifications of the

Ricci curvature In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measur ...

of the Riemannian manifold, as introduced by

Dominique Bakry Roger-Dominique Bakry (born 12 December 1954), known as Dominique Bakry, is a French mathematician, a professor at the Université Paul-Sabatier in Toulouse, and a senior member of Institut Universitaire de France. Bakry graduated from , and pre ...

and Michel Émery.D. Bakry and Michel Émery. Diffusions hypercontractives. Séminaire de probabilités, XIX, 1983/84, 177–206. Lecture Notes in Math., 1123, Springer, Berlin, 1985. Morgan showed how to modify the classical Heintze-Karcher inequality, which controls the volume of certain cylindrical regions in the space by the Ricci curvature in the region and the

mean curvature In mathematics, the mean curvature H of a surface S is an ''extrinsic'' measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space. T ...

of the region's cross-section, to hold in the setting of manifolds with density. As a corollary, he was also able to put the Levy-Gromov

isoperimetric inequality In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n-dimensional space \R^n the inequality lower bounds the surface area or perimeter \operatorname(S) of a set S\subset\R^n ...

into this setting. Much of his current work deals with various aspects of isoperimetric inequalities and manifolds with density.

Publications

Textbooks

*''Calculus Lite.'' Third edition. A K Peters/CRC Press, Natick, MA, 2001. *''Geometric measure theory. A beginner's guide.'' Fifth edition. Illustrated by James F. Bredt. Elsevier/Academic Press, Amsterdam, 2016. viii+263 pp. *''The math chat book.'' MAA Spectrum. Mathematical Association of America, Washington, DC, 2000. xiv+113 pp. *''Real analysis.'' American Mathematical Society, Providence, RI, 2005. viii+151 pp. *''Real analysis and applications. Including Fourier series and the calculus of variations.'' American Mathematical Society, Providence, RI, 2005. x+197 pp. *''Riemannian geometry. A beginner's guide.'' Second edition. A K Peters, Ltd., Wellesley, MA, 1998. x+156 pp.

Notable articles

* Michael Hutchings, Frank Morgan, Manuel Ritoré, and Antonio Ros. Proof of the double bubble conjecture. Ann. of Math. (2) 155 (2002), no. 2, 459–489. doi:10.2307/3062123 * Frank Morgan
Manifolds with density.
Notices Amer. Math. Soc. 52 (2005), no. 8, 853–858.

Notes

External links

*
Williams College home page
{{DEFAULTSORT:Morgan, Frank Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians Massachusetts Institute of Technology alumni Princeton University alumni Massachusetts Institute of Technology School of Science faculty Williams College faculty Fellows of the American Mathematical Society American textbook writers Geometers Measure theorists