# Isometric immersions and beyond

Monday, November 2, 2015 - 3:30pm - 4:30pm

Keller 3-180

László Székelyhidi Jr. (Universität Leipzig)

Nash wrote three papers on isometric embeddings of Riemannian manifolds in the Euclidean space, which

are landmark papers not only for the mathematical problem they solved, but more importantly because of the impact they had on other fields, encompassing applications that go well beyond differential geometry. In these papers Nash introduced two iteration schemes, which both lead to a tremendous amount of further development: the Nash-Moser hard implicit function theorem and the convex integration scheme of Gromov. In particular the latter has seen a recent revival not only for isometric embeddings, but also for the construction of weak solutions of the incompressible Euler equations in a way that very closely resembles Nash's original proof.

are landmark papers not only for the mathematical problem they solved, but more importantly because of the impact they had on other fields, encompassing applications that go well beyond differential geometry. In these papers Nash introduced two iteration schemes, which both lead to a tremendous amount of further development: the Nash-Moser hard implicit function theorem and the convex integration scheme of Gromov. In particular the latter has seen a recent revival not only for isometric embeddings, but also for the construction of weak solutions of the incompressible Euler equations in a way that very closely resembles Nash's original proof.

MSC Code:

46B04