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Approximations of curvature functionals

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Critical points of curvature functionals such as the Dirichlet energy and the Willmore energy are of great interest in geometric analysis. Unfortunately these functionals don’t satisfy the Palais Smale condition due to their conformal invariance. In ‘81 Sacks and Uhlenbeck introduced the alpha-approximation of the Dirichlet energy to evade this problem. In this talk we examine a similar approximation for the Ricci energy and study the regularity of critical points. This is based on joint work with Reto Buzano and Tobias Lamm.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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