A Minimal Lamination of the Interior of a Positive Cone with Quadratic Curvature Blowup

Logarithmically spiraling helicoids

“…This formalization is extremely useful and helps streamline the presentation since almost every geometric quantity we estimate-the mean curvature, e.g.-is such a quantity. The discussion generalizes a similar one in [2].…”

“…The functionĒ can then be solved for by direct integration. In particular, in [2] we proved that the the expressionv satisfies cosh 2 (s)L Fv =Ē. Moreover, by Lemma 8 of [2], making the appropriate modifications for the norms of interest here, we establish there exists a uniform C > 0 such that v : X 2 ≤ C Ē : X 0 .…”

“…Comparing immersions on spirals with straight lines. In [2], we considered immersions of the form: ). There are constants ǫ 0 , δ 0 > 0 sufficiently small so that for any 0 < δ < δ 0 , there is a function u 0δ (s) : [−ǫ 0 δ −1/4 , ǫ 0 δ −1/4 ] → R such that:…”

“…Comparing immersions on spirals with straight lines. In [2], we considered immersions of the form: G 0δ (s, θ) = e δθ sin(θ) sinh(s), e δθ cos(θ) sinh(s), 1 δ e δθ . (4.1) Theorem 4.3 (Theorem 1 from [2]).…”

“…In [2], we considered immersions of the form: G 0δ (s, θ) = e δθ sin(θ) sinh(s), e δθ cos(θ) sinh(s), 1 δ e δθ . (4.1) Theorem 4.3 (Theorem 1 from [2]). There are constants ǫ 0 , δ 0 > 0 sufficiently small so that for any 0 < δ < δ 0 , there is a function u 0δ (s) : [−ǫ 0 δ −1/4 , ǫ 0 δ −1/4 ] → R such that:…”