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.
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© 1984 Springer Science+Business Media New York
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Giusti, E. (1984). Regularity of Minimal Surfaces. In: Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, vol 80. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4684-9486-0_8
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DOI: https://doi.org/10.1007/978-1-4684-9486-0_8
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-3153-6
Online ISBN: 978-1-4684-9486-0
eBook Packages: Springer Book Archive