We explore the relationship between contact forms on $\mathbb S^3$ defined by Finsler metrics on $\mathbb S^2$ and the theory developed by H. Hofer, K. Wysocki and E. Zehnder in \cite{HWZ,HWZ1}. We show that a Finsler metric on $\mathbb S^2$ with curvature $K\geq 1$ and with all geodesic loops of length $>\pi$ is dynamically convex and hence it has either two or infinitely many closed geodesics. We also explain how to explicitly construct $J$-holomorphic embeddings of cylinders asymptotic to...
Source: http://arxiv.org/abs/math/0701616v1