# Mathematician:Karen Keskulla Uhlenbeck

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## 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

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)

- 1991:

- 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.