A TOUR THROUGH $\delta$-INVARIANTS: FROM NASH'S EMBEDDING THEOREM TO IDEAL IMMERSIONS, BEST WAYS OF LIVING AND BEYOND$^{ 1}$

Bang-Yen Chen

Abstract: First I will explain my motivation to introduce the $\delta$-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 $\delta$-invariants to several areas in mathematics. Finally, I will present two optimal inequalities involving $\delta$-invariants for Lagrangian submanifolds obtained very recently in joint papers with F. Dillen, J. Van der Veken and L. Vrancken.

Classification (MSC2000): 52-02, 53A07; 35P15, 53B21, 53C40, 92K99

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