Local well-posedness of critical nonlinear Schrodinger equation on Zoll manifolds of odd-growth

In this paper, we study the nonlinear Schrodinger equation on Zoll manifolds with odd order nonlinearities. We will obtain the local well-poesdness in the critical space Hs0(M). This extends the recent results in the literature to the Zoll manifolds of dimension d2 with general odd order nonlinearities and also partially improves the previous results in the subcritical spaces of Yang to the critical cases. Copyright (c) 2015 John Wiley & Sons, Ltd.