The Gromov width of complex Grassmannians

We show that the Gromov width of the Grassmannian of complex k -planes in C n is equal to one when the symplectic form is normalized so that it generates the integral cohomology in degree 2. We deduce the lower bound from more general results.For example, if a compact manifold N with an integral symplectic form ω admits a Hamiltonian circle action with a fixed point p such that all the isotropy weights at p are equal to one, then the Gromov width of (N, ω) is at least one.We use holomorphic techniques to prove the upper bound.