Summary
Doris Fischer-Colbrie is a ceramic artist and former mathematician.[1] She received her Ph.D. in mathematics in 1978 from University of California at Berkeley, where her advisor was H. Blaine Lawson.[2]
Many of her contributions to the theory of minimal surfaces are now considered foundational to the field. In particular, her collaboration with Richard Schoen is a landmark contribution to the interaction of stable minimal surfaces with nonnegative scalar curvature.[3] A particular result, also obtained by Manfredo do Carmo and Chiakuei Peng, is that the only complete stable minimal surfaces in ℝ3 are planes.[4] Her work on unstable minimal surfaces gave the basic tools by which to relate the assumption of finite index to conditions on stable subdomains and total curvature.[5][6]
After positions at Columbia University and San Diego State University, Fischer-Colbrie left academia to become a ceramic artist. She is married to Schoen, with whom she has two children.[7]
Publication list edit
- Fischer-Colbrie, D. (1980). "Some rigidity theorems for minimal submanifolds of the sphere". Acta Mathematica. 145 (1–2): 29–46. doi:10.1007/BF02414184. MR 0558091. Zbl 0464.53047.
- Fischer-Colbrie, Doris; Schoen, Richard (1980). "The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature". Communications on Pure and Applied Mathematics. 33 (2): 199–211. CiteSeerX 10.1.1.1081.96. doi:10.1002/cpa.3160330206. MR 0562550. Zbl 0439.53060.
- Fischer-Colbrie, D. (1985). "On complete minimal surfaces with finite Morse index in three-manifolds". Inventiones Mathematicae. 82 (1): 121–132. doi:10.1007/BF01394782. MR 0808112. Zbl 0573.53038.
References edit
- ^ "Doris Fischer-Colbrie". dorisfischer-colbrie.com.
- ^ Doris Fischer-Colbrie at the Mathematics Genealogy Project
- ^ Li, Peter. Geometric analysis. Cambridge Studies in Advanced Mathematics, 134. Cambridge University Press, Cambridge, 2012. x+406 pp. ISBN 978-1-107-02064-1
- ^ do Carmo, M.; Peng, C. K. Stable complete minimal surfaces in ℝ3 are flat planes. Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 6, 903–906.
- ^ Meeks, William H., III; Pérez, Joaquín The classical theory of minimal surfaces. Bull. Amer. Math. Soc. (N.S.) 48 (2011), no. 3, 325–407.
- ^ Meeks, William H., III; Pérez, Joaquín. A survey on classical minimal surface theory. University Lecture Series, 60. American Mathematical Society, Providence, RI, 2012. x+182 pp. ISBN 978-0-8218-6912-3
- ^ The mathematics of Richard Schoen. Notices Amer. Math. Soc. 65 (2018), no. 11, 1349–1376.