of convex curves in
Author: Martin Bridgeman
Journal: Proc. Amer. Math. Soc. 126 (1998), 221-224
MSC (1991): Primary 51M09, 52A55; Secondary 52A38, 52A15
MathSciNet review: 1415576
Full-text PDF Free Access
Abstract: A well-known result states that, if a curve in has geodesic curvature less than or equal to one at every point, then is embedded. The converse is obviously not true, but the embeddedness of a curve does give information about the curvature. We prove that, if is a convex embedded curve in , then the average curvature (curvature per unit length) of , denoted , satisfies . This bound on the average curvature is tight as for a horocycle.
- M. Bridgeman, Average bending of boundaries of convex cores, In preparation.
- M. Spivak, A Comprehensive Introduction to Differential Geometry, Volume III, Publish or Perish (1979). MR 82g:53003c
Received by editor(s): June 13, 1996
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1998 American Mathematical Society