Seminar: Johanna Bimmermann (G.15.25)
Symmetric R-spaces N are compact-type symmetric spaces that appear as real forms of Hermitian symmetric spaces N_C. Consequently, N sits inside N_C as a Lagrangian submanifold. Weinstein’s tubular neighborhood theorem provides a local symplectic identification between a neighborhood of the zero section in the (co-)tangent bundle TN and a neighborhood of N in N_C. In this talk, we show that this symplectic neighborhood is, in fact, open-dense and can be interpreted as a kind of (dual) Grauert domain in TN. We compute symplectic invariants of these domains, namely the Gromov width and the Hofer–Zehnder capacity.
