Lawson found in 1970 a method to solve free boundary value problems for unstable Euclidean constant-mean-curvaturesurfaces by solving a corresponding Plateau problem for minimal surfaces in S3. 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 geometry
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.
Lawson, H. Blaine Jr. (1969). "Local rigidity theorems for minimal hypersurfaces". Annals of Mathematics. Second Series. 89 (1): 187–197. doi:10.2307/1970816. JSTOR 1970816. MR 0238229. Zbl 0174.24901.
Lawson, H. Blaine Jr. (1970). "Complete minimal surfaces in S3". Annals of Mathematics. Second Series. 92 (3): 335–374. doi:10.2307/1970625. JSTOR 1970625. MR 0270280. Zbl 0205.52001.
Hsiang, Wu-yi; Lawson, H. Blaine Jr. (1971). "Minimal submanifolds of low cohomogeneity". Journal of Differential Geometry. 5 (1–2): 1–38. doi:10.4310/jdg/1214429775. MR 0298593. Zbl 0219.53045.
Lawson, H. Blaine Jr.; Yau, Shing Tung (1972). "Compact manifolds of nonpositive curvature". Journal of Differential Geometry. 7 (1–2): 211–228. doi:10.4310/jdg/1214430828. MR 0334083. Zbl 0266.53035.
Lawson, H. Blaine Jr.; Simons, James (1973). "On stable currents and their application to global problems in real and complex geometry". Annals of Mathematics. Second Series. 98 (3): 427–450. doi:10.2307/1970913. JSTOR 1970913. MR 0324529. Zbl 0283.53049.
Harvey, F. Reese; Lawson, H. Blaine Jr. (1975). "On boundaries of complex analytic varieties. I". Annals of Mathematics. Second Series. 102 (2): 223–290. doi:10.2307/1971032. JSTOR 1971032. MR 0425173. Zbl 0317.32017.
Gromov, Mikhael; Lawson, H. Blaine Jr. (1980). "Spin and scalar curvature in the presence of a fundamental group. I". Annals of Mathematics. Second Series. 111 (2): 209–230. doi:10.2307/1971198. JSTOR 1971198. MR 0569070. Zbl 0445.53025.
Gromov, Mikhael; Lawson, H. Blaine Jr. (1980). "The classification of simply connected manifolds of positive scalar curvature". Annals of Mathematics. Second Series. 111 (3): 423–434. doi:10.2307/1971103. JSTOR 1971103. MR 0577131. Zbl 0463.53025.
Lawson, H. Blaine Jr. (1980). Lectures on minimal submanifolds. Vol. I. Mathematics Lecture Series. Vol. 9 (Second edition of 1977 original ed.). Wilmington, DE: Publish or Perish, Inc. ISBN 0-914098-18-7. MR 0576752. Zbl 0434.53006.
Lawson, H. Blaine Jr. (1985). The theory of gauge fields in four dimensions. CBMS Regional Conference Series in Mathematics. Vol. 58. Providence, RI: American Mathematical Society. doi:10.1090/cbms/058. ISBN 0-8218-0708-0. MR 0799712. Zbl 0597.53001.