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Minimal Surfaces in Riemannian Manifolds
Min Ji and Guang Yin Wang
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Memoirs of the American Mathematical Society
1993; 50 pp; softcover
Volume: 104
ISBN-10: 0-8218-2560-7
ISBN-13: 978-0-8218-2560-0
List Price: US$28
Individual Members: US$16.80
Institutional Members: US$22.40
Order Code: MEMO/104/495
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This monograph studies the structure of the set of all coboundary minimal surfaces in Riemannian manifolds. The authors establish, on a solid analytical foundation, a flexible topological index theory which proves useful for the study of minimal surfaces. One of the highlights of the work is the result that for every Jordan curve on the standard \(n\)-sphere, there exist at least two minimal surfaces bounded by the curve.

Readership

Research mathematicians.

Table of Contents

  • Introduction
  • Preliminaries
  • Compactness and regularity
  • A priori estimates
  • Conformality and deformation lemmas for \(E\)
  • Mountain-pass-solution
  • A minimax principle
  • References
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