 
Summary: Vol. 96, No. 2 DUKE MATHEMATICAL JOURNAL (C) 1999
FINITE ENERGY SURFACES AND THE
CHORD PROBLEM
C. ABBAS
CONTENTS
1. Introduction 241
2. Finite energy halfplanes and orbits of the Reeb vector field 249
3. Asymptotic behaviour of nondegenerate finite energy halfplanes 263
3.1. Convergence at infinity 263
3.2. Exponential decay estimates 266
3.3. A representation formula 291
1. Introduction. A contact form on an odddimensional manifold M of
dimension 2n + 1 is a 1form 2 such that the (2n + 1)form fl, given by
^ ",
defines a volume form on M. We observe that any manifold admitting a contact
form is necessarily orientable and that a contact form defines a natural
orientation.
Assume now that (M, 2) is a manifold together with a given contact form.
First of all, we note that 2 defines a 2ndimensional vector bundle over M.
Indeed, consider M, where is given by
