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Regularity of Minimal Surfaces

  • Enrico Giusti
Part of the Monographs in Mathematics book series (MMA, volume 80)

Abstract

In this chapter we can finally prove that partial regularity of minimal surfaces; namely we show that the reduced boundary ∂*E is analytic and the only possible singularities must occur in ∂E – ∂*E. Our major task in the following chapters will be to obtain an estimate for the size of ∂E – ∂*E. As mentioned before, the main step in the regularity theory is the De Giorgi lemma. We show that a minimal surface is regular at points which satisfy the hypotheses of the lemma. Obviously by the definition of reduced boundary this must include all the points in ∂*E and we show that the converse also holds and further that ∂*E is relatively open in ∂E.

Keywords

Differential Equation Partial Differential Equation Minimal Surface Main Step Standard Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • Enrico Giusti

There are no affiliations available

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