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Behavior of distant maximal geodesics in finitely connected complete $2$-dimensional Riemannian manifolds

About this Title

Takashi Shioya

Publication: Memoirs of the American Mathematical Society
Publication Year: 1994; Volume 108, Number 517
ISBNs: 978-0-8218-2578-5 (print); 978-1-4704-0094-1 (online)
DOI: https://doi.org/10.1090/memo/0517
MathSciNet review: 1185879
MSC: Primary 53C22; Secondary 58E10

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Table of Contents

Chapters

  • Introduction
  • 1. The semi-regular curves in a differentiable plane
  • 2. Statement of main results and examples
  • 3. Some applications of the Gauss-Bonnet theorem
  • 4. Semi-regularity of distant geodesics
  • 5. Almost regularity of distant geodesics
  • 6. The visual diameter
  • 7. Distant geodesics in a finitely connected manifold with finitely connected boundary