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Morse theory and rigidity for the Monge—Ampère equation

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If you have a question about this talk, please contact Zoe Wyatt .

I will begin by giving a brief overview of rigidity and flexibility results in nonlinear PDE , a prime example being the case of isometric embeddings. In two dimensions, the rigidity/flexibility of isometric embeddings is closely related to rigidity/flexibility of non-convex solutions to the Monge-Ampère equation. I will then discuss a recent result, obtained with R. Tione, which gives a complete rigidity result for solutions of the Monge-Ampère equation in general dimension, as conjectured by Šverák in 1992. The proof relies on Morse theory for non-smooth functions.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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