Contents
Abstract viii
Acknowledgement ix
Introduction 1
1. The semi-regular curves in a differentiable plane 5
2. Statement of main results and examples 14
3. Some applications of the Gauss-Bonnet theorem 26
4. Semi-regularity of distant geodesies 46
5. Almost regularity of distant geodesies 5 3
6. The visual diameter 62
7. Distant geodesies in a finitely connected manifold
with finitely connected boundary 69
References 72
vn
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