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Karen Uhlenbeck and the calculus of variations. (English) Zbl 1420.49001

The purpose of this article is to conduct an in-depth discussion of a group of works, primarily from the 1980s, firstly written by Karen Uhlenberg, who focused on variational problems in differential geometry. According to this discussion, the whole circle of ideas and techniques involving the dimension of singular sets, monotonicity, the “small energy” results, tangent cones, etc., has had a considerable impact on many branches of differential geometry over the past few decades and forms the focus of much current research activity. In addition to the cases of harmonic maps and Yang-Mills fields, the minimal theory of the submanifold in which many ideas have emerged and the theory of the convergence of Riemannian metrics with the Ricci curvature bounds are notable examples.

MSC:

49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control
49-03 History of calculus of variations and optimal control
01A70 Biographies, obituaries, personalia, bibliographies
58E30 Variational principles in infinite-dimensional spaces

Biographic References:

Uhlenbeck, Karen
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