Mathematician:Karen Keskulla Uhlenbeck

Mathematician

American mathematician who is one of the founders of modern geometric analysis.

Abel Prize

Karen Keskulla Uhlenbeck was awarded an Abel Prize in $\text {2019}$:

For her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.

Nationality

American

History

• Born: August 24, 1942 in Cleveland, Ohio, U.S.

Theorems and Definitions

• Donaldson-Uhlenbeck-Yau Theorem (with Simon Kirwan Donaldson and Shing-Tung Yau)

Results named for Karen Keskulla Uhlenbeck can be found here.

Publications

• 1977: Regularity for a class of non-linear elliptic systems (Acta Math. Vol. 138: pp. 219 – 240)

• 1981: The existence of minimal immersions of 2-spheres (Ann. Math. Ser. 2 Vol. 113: pp. 1 – 24) (with Jonathan Sacks)  www.jstor.org/stable/1971131

• 1982: Minimal immersions of closed Riemann surfaces (Trans. Amer. Math. Soc. Vol. 271: pp. 639 – 652) (with J. Sacks)  www.jstor.org/stable/1998902

• 1982: Removable singularities in Yang-Mills fields (Commun. Math. Phys. Vol. 83: pp. 11 – 29)

• 1982: Connections with $L^p$ bounds on curvature (Commun. Math. Phys. Vol. 83: pp. 31 – 42)

• 1982: A regularity theory for harmonic maps (J. Differ. Geom. Vol. 17: pp. 307 – 335) (with Richard Schoen)

• 1984: Instantons and Four-Manifolds (with Daniel S. Freed)
  • 1991: Instantons and Four-Manifolds 2nd ed. (with Daniel S. Freed)

• 1986: On the existence of Hermitian-Yang-Mills connections in stable vector bundles (Communications on Pure and Applied Mathematics Vol. 39: pp. S257 – S293) (with Shing-Tung Yau)

• 1989: Harmonic maps into Lie groups: classical solutions of the chiral model (J. Differ. Geom. Vol. 30: pp. 1 – 50)

• 1992: On the connection between harmonic maps and the self-dual Yang-Mills and the sine-Gordon equations (Journal of Geometry and Physics Vol. 8: pp. 283 – 316)

Also known as

Born Karen Keskulla, she adopted the surname Uhlenbeck on her marriage to Olke C. Uhlenbeck.

Sources

• John J. O'Connor and Edmund F. Robertson: "Karen Keskulla Uhlenbeck": MacTutor History of Mathematics archive