Curriculum Vitae

John Douglas Moore

Birthplace: Chicago, Illinois, USA
Birthdate: July 11, 1943
Citizenship: USA

EDUCATION

BA, University of California, Berkeley, CA 1965
PhD, University of California, Berkeley, CA 1969

PROFESSIONAL EXPERIENCE

Assistant Professor, University of California, Santa Barbara, CA 1969-1975
Associate Professor, University of California, Santa Barbara, CA 1975-1981
Professor, University of California, Santa Barbara, CA 1981-present
Chair, Department of Mathematics, University of California, Santa Barbara, CA 1999-2004.

On the left, at the Great Wall near

Beijing in 2002. On the right, playing

Chopin in the summer of 2007.



RESEARCH INTERESTS

My research interests center on curvature and topology of submanifolds in Euclidean space, and applications of minimal surfaces to Riemannian geometry. For example, one of my theorems shows that compact Riemannian manifolds which have positive sectional curvature and admit codimension two isometric immersions in Euclidean space must be homeomorphic to spheres. The proof, first presented in 1978, is based upon Morse theory of the height function.

In collaboration with Mario Micallef, I gave a proof of the sphere theorem from Riemannian geometry (1988) using minimal surfaces. The proof shows that the relevant curvature for the study of stability of minimal surfaces in Riemannian manifolds is the isotropic sectional curvature. In fact, the argument shows that a compact simply connected Riemannian manifold with positive isotropic curvature of dimension at least four must be homeomorphic to a sphere. This extends an earlier sphere theorem of Berger, Klingenberg and Toponogov, which was proven using geodesics instead of minimal surfaces.

Recent research has focused on developing a partial Morse theory for closed minimal surfaces in Riemannian manifolds. The first step is the bumpy metric theorem presented in a preprint available from the mathematics archive.


SELECTED PUBLICATIONS

1971 "Isometric immersions of Riemannian products," J. Differential Geometry v. 5, pp. 159--168.
1972 "Isometric immersions of space forms in space forms," Pacific J. Math. v. 40, pp. 157--166.
1977 "Conformally flat submanifolds of Euclidean space," Math. Ann. v. 225, pp. 89--97.
1977 "Submanifolds of constant positive curvature I," Duke Math. J. v. 44, pp. 449--484.
1978 "Codimension two submanifolds of positive curvature," Proc. Amer. Math. Soc. v. 70, pp. 72--74.
1980 "On equivariant isometric embeddings," (with Roger Schlafly), Math. Z. v. 173, pp. 125--141.
1985 "On stability of minimal spheres and a two-dimensional version of Synge's theorem," Arch. Math. v. 44, pp. 278--281.
1986 "Compact Riemannian manifolds with positive curvature operators," Bull. Amer. Math. Soc. v. 14, pp. 279--282.
1988 "Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes," (with Mario Micallef) Annals of Math. v. 127, pp. 199--227.
1990 "On the number of minimal two-spheres of small area in manifolds with curvature bounded above," Math. Ann. v. 288, pp. 323--343.
1996 "On extendability of isometric immersions of spheres," Duke Math. J. v. 85, pp. 685--699.
2001 "Lectures on Seiberg-Witten invariants," second edition, Springer, New York. Revised version.
2002 "Euler characters and submanifolds of constant positive curvature," Trans. Amer. Math. Soc., v. 354, pp. 3815--3834.
2006 "Bumpy metrics and closed parametrized minimal surfaces in Riemannian manifolds," Trans. Amer. Math. Soc., v. 358, pp. 5193-5256; correction, Trans. Amer. Math. Soc., v. 359, pp. 5117-5123. Revised version.
2007 "Nondegeneracy of coverings of minimal tori and Klein bottles in Riemannian manifolds," Pacific J. Math., v. 230, pp. 147-166.
2007 "Second variation of energy for minimal surfaces in Riemannian manifolds," Matematica Contemporanea, v. 33, pp. 213-241.

PREPRINTS IN PDF FORMAT

2007 "Energy growth in minimal surface bubbles," to appear.
2010 "Bumpy metrics and closed parametrized minimal surfaces in Riemannian manifolds, revised version," arXiv preprint 1012.3906.
2010 "Lecture notes on global analysis," preliminary version.