2010
DOI: 10.1016/j.aim.2010.02.007
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The Codazzi equation for surfaces

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Cited by 33 publications
(88 citation statements)
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“…Remark 1. Case I in the above result has also been proved in [2] on the additional assumption that ψ is properly embedded.…”
Section: )mentioning
confidence: 77%
“…Remark 1. Case I in the above result has also been proved in [2] on the additional assumption that ψ is properly embedded.…”
Section: )mentioning
confidence: 77%
“…τ = 0, such Codazzi pair was found a long time ago (cf. [3]). Our goal here is to obtain a Codazzi pair on any H−surface such that the Abresch-Rosenberg differential appears as its Hopf differential.…”
Section: Abresch-rosenberg Differential and Codazzi Pairsmentioning
confidence: 99%
“…Consider the quadratic form II S associated to S given by (17). In [3], it was shown that (I, II S ) is a Codazzi pair on Σ if H is constant. Moreover, it is traceless, i.e., tr(S) = 0 = H(I, II S ), and the Hopf differential associated to (I, II S ) is the Abresch-Rosenberg differential Q AR in M 2 (κ) × R.…”
Section: Abresch-rosenberg Differential and Codazzi Pairsmentioning
confidence: 99%
“…The technique used in [2] to prove a geometric height estimate for SWET surfaces in M 3 (c), c ≤ 0, does not apply to our setting. Theorem 6.2 in [6] provides a horizontal height estimate for compact surfaces Σ with constant curvature or constant mean curvature in H 2 (c) × R and boundary contained in a vertical plane.…”
Section: Corollary 12 (Height Estimate For Cmc Surfaces)mentioning
confidence: 99%
“…They followed the ideas of Meeks [11] and Korevaar-Kusner-Solomon [10] for non-zero constant mean curvature surfaces in R 3 . Recently, Aledo-Espinar-Gálvez in [2] obtained a geometric height estimate for SWET surfaces with f (0) = 0 in M 3 (c), c ≤ 0, with no other hypothesis on f.…”
Section: Introductionmentioning
confidence: 99%