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arxiv: 1404.6996 · v2 · pith:263VVX72new · submitted 2014-04-28 · 🧮 math.DG · math.AP

Logarithmically spiraling helicoids

classification 🧮 math.DG math.AP
keywords curvesembeddedlogarithmicsurfacesalongaxesconeconstruct
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We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves and the nature of the construction. Moreover, inside of a "logarithmic cone", the surfaces are embedded.

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