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Blaschke’s rolling theorem in $R^{n}$

About this Title

J. N. Brooks and J. B. Strantzen

Publication: Memoirs of the American Mathematical Society
Publication Year: 1989; Volume 80, Number 405
ISBNs: 978-0-8218-2466-5 (print); 978-1-4704-0828-2 (online)
DOI: https://doi.org/10.1090/memo/0405
MathSciNet review: 974998
MSC: Primary 52A20

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Table of Contents

Chapters

  • Part I. Local conditions for containment
  • 0. Introduction
  • 1. Main result and sketch proof
  • 2. The main result for curves
  • 3. Convex regions in $\mathbf {R}^n$
  • 4. The smooth case: Applications to differential geometry
  • Part II. Common boundaries of touching convex regions and Blaschke’s rolling theorem
  • 5. Introduction
  • 6. Some preliminaries
  • 7. Existence of hyperplanes of support
  • 8. Common boundaries results
  • 9. Application to spheres and Blaschke’s rolling theorem