Poisson Lie Groups and Non-Linear Convexity Theorems

In this paper we describe how one can derive nonlinear convexity theorems which are similar to Kostant's nonlinear convexity theorem for the Iwasawa decomposition from Hamiltonian actions on Poisson Lie groups. Our results generalize those of LU and Ratiu (24]) and aim at a unified symplectic framework for the convexity theorem in 32] and the linear convexity theorems for coadjoint orbits of convex type in 15].