TABLE OF CONTENTS
Part I
Local Conditions for Containment
Chapter Page
0. INTRODUCTION 1
1. MAIN RESULT AND SKETCH PROOF 2
1.1 Definitions and Statement of Main Result 2
2. THE MAIN RESULT FOR CURVES 6
2.1 Preliminary Results and Notation 6
2.2 The Main Result for Curves 7
3. CONVEX REGIONS IN R n 21
3.1 Preliminary Results 21
3.2 Faithful Projections 23
3.3 Proving Lemma 1.1.5 26
3.4 Proving Theorem 1.1.4 33
3.5 Possible Generalisations of the Main Theorem 41
4. THE SMOOTH CASE: APPLICATIONS TO DIFFERENTIAL GEOMETRY 47
4.1 Local Representation of 5 as a Function 47
4.2 Radii of Curvature Indicatrices 48
4.2 Semi-Local Insideness in Terms of Radii of Curvature and Indicatrices 50
continued over page
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