3 problems

Let $N$ and $L$ be closed, simply connected manifolds of the same dimension. The cotangent bundle $T^*N$ carries its natural symplectic structure, and consider the space of Lagrang…

For $a\ge1$, define the embedding capacity … Here $E^4(1,a)$ and $B^k(r)$ are the standard symplectic ellipsoid and ball, respectively. The Lagrangian embedding capacity identity.…

Let $L$ and $N$ be simply connected manifolds, and let $ST^*L$ denote the unit cotangent sphere bundle of $L$, viewed as a contact manifold embedded in $T^*N$. An exact Lagrangian…