Memoirs of the American Mathematical Society 1994; 73 pp; softcover Volume: 108 ISBN10: 082182578X ISBN13: 9780821825785 List Price: US$37 Individual Members: US$22.20 Institutional Members: US$29.60 Order Code: MEMO/108/517
 This monograph studies the topological shapes of geodesics outside a large compact set in a finitely connected, complete, and noncompact surface admitting total curvature. When the surface is homeomorphic to a plane, all such geodesics behave like those of a flat cone. In particular, the rotation numbers of the geodesics are controlled by the total curvature. Accessible to beginners in differential geometry, but also of interest to specialists, this monograph features many illustrations that enhance understanding of the main ideas. Readership Graduate students studying differential geometry for the first time as well as specialists in the field. Table of Contents  Introduction
 The semiregular curves in a differentiable plane
 Statement of main results and examples
 Some applications of the GaussBonnet theorem
 Semiregularity of distant geodesics
 Almost regularity of distant geodesics
 The visual diameter
 Distant geodesics in a finitely connected manifold with finitely connected boundary
 References
