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Vol. 96, No. 2 DUKE MATHEMATICAL JOURNAL (C) 1999 FINITE ENERGY SURFACES AND THE
 

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 half-planes and orbits of the Reeb vector field 249
3. Asymptotic behaviour of nondegenerate finite energy half-planes 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 odd-dimensional manifold M of
dimension 2n + 1 is a 1-form 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 2n-dimensional vector bundle over M.
Indeed, consider M, where is given by

  

Source: Abbas, Casim - Department of Mathematics, Michigan State University

 

Collections: Mathematics