# H. Blaine Lawson

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**Herbert Blaine Lawson, Jr.** is a mathematician best known for his work in minimal surfaces, calibrated geometry, and algebraic cycles. He is currently a Distinguished Professor of Mathematics at Stony Brook University. He received his PhD from Stanford University in 1969 for work carried out under the supervision of Robert Osserman.^{[3]}

H. Blaine Lawson, Jr. | |
---|---|

H. Blaine Lawson in Berkeley, 1972 | |

Born | ^{[1]}Norristown, Pennsylvania ^{[2]} | January 4, 1942

Citizenship | United States |

Awards | Leroy P. Steele Prize (1975) |

Scientific career | |

Fields | Algebraic cycles Calibrated geometry Minimal surfaces |

Institutions | Stony Brook University |

Doctoral advisor | Robert Osserman |

Doctoral students | Michael T. Anderson William Meeks, III Doris Fischer-Colbrie |

## ResearchEdit

### Minimal surfacesEdit

Lawson found in 1970 a method to solve free boundary value problems for unstable Euclidean constant-mean-curvature surfaces by solving a corresponding Plateau problem for minimal surfaces in *S*^{3}. He constructed compact minimal surfaces in the 3-sphere of arbitrary genus by applying Charles B. Morrey, Jr.'s solution of the Plateau problem in general manifolds. This work of Lawson contains a rich set of ideas, among them the conjugate surface construction for minimal and constant mean curvature surfaces.

### Calibrated geometryEdit

The theory of calibrations, whose roots are in the work of Marcel Berger, finds its genesis in a 1982 *Acta Mathematica* paper of
Reese Harvey and Blaine Lawson. The theory of calibrations has grown to be important because of its many applications to gauge theory and mirror symmetry.

### Algebraic cyclesEdit

In his 1989 *Annals of Mathematics* paper "Algebraic Cycles and Homotopy Theory", Lawson proved a theorem which is now called the Lawson suspension theorem. This theorem is the cornerstone of Lawson homology and morphic cohomology which are defined by taking the homotopy groups of algebraic cycle spaces of complex varieties.

These two theories are dual to each other for smooth varieties and have properties similar to those of Chow groups.

## Awards and honorsEdit

He was a 1973 recipient of the American Mathematical Society's Leroy P. Steele Prize, and was elected to the National Academy of Sciences in 1995. He is a former recipient of both the Sloan Fellowship and the Guggenheim Fellowship, and has delivered two invited addresses at International Congresses of Mathematicians, one on geometry, and one on topology. He has served as Vice President of the American Mathematical Society, and is a foreign member of the Brazilian Academy of Sciences.

In 2012 he became a fellow of the American Mathematical Society.^{[4]} He was elected to the American Academy of Arts and Sciences in 2013.^{[5]}

## Major publicationsEdit

- Lawson, H. Blaine, Jr.
*Local rigidity theorems for minimal hypersurfaces.*Ann. of Math. (2) 89 (1969), 187–197. - Lawson, H. Blaine, Jr.
*Complete minimal surfaces in S3.*Ann. of Math. (2) 92 (1970), 335–374. - Hsiang, Wu-yi; Lawson, H. Blaine, Jr.
*Minimal submanifolds of low cohomogeneity.*J. Differential Geometry 5 (1971), 1–38. - Harvey, F. Reese; Lawson, H. Blaine, Jr.
*On boundaries of complex analytic varieties. I.*Ann. of Math. (2) 102 (1975), no. 2, 223–290. - Gromov, Mikhael; Lawson, H. Blaine, Jr.
*The classification of simply connected manifolds of positive scalar curvature.*Ann. of Math. (2) 111 (1980), no. 3, 423–434. - Harvey, Reese; Lawson, H. Blaine, Jr.
*Calibrated geometries.*Acta Math. 148 (1982), 47–157. - Gromov, Mikhael; Lawson, H. Blaine, Jr.
*Positive scalar curvature and the Dirac operator on complete Riemannian manifolds.*Inst. Hautes Études Sci. Publ. Math. No. 58 (1983), 83–196 (1984).

## ReferencesEdit

**^**Date information sourced from Library of Congress Authorities data, via corresponding WorldCat Identities linked authority file (LAF).**^**"Lawson, Herbert Blaine".*American Men and Women of Science*. vol. 4 (21st ed.). Bowker. 2009.**^**H. Blaine Lawson at the Mathematics Genealogy Project**^**List of Fellows of the American Mathematical Society, retrieved 2013-01-27.**^**Newly elected members Archived 2013-05-01 at the Wayback Machine, American Academy of Arts and Sciences, April 2013, retrieved 2013-04-24.