A tour through $δ$-invariants: From Nash's embedding theorem to ideal immersions, best ways of living and beyond

First I will explain my motivation to introduce the $δ$-invariants for Riemannian manifolds. I will also recall the notions of ideal immersions and best ways of living. Then I will present a few of the many applications of $δ$-invariants to several areas in mathematics. Finally, I will present two optimal inequalities involving $δ$-invariants for Lagrangian submanifolds obtained very recently in joint papers with F. Dillen, J. Van der Veken and L. Vrancken.

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