Communications in Analysis and Geometry
Volume 26 (2018)
Logarithmically spiraling helicoids
Pages: 461 – 504
We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals using PDE methods. 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.
differential geometry, minimal surfaces, partial differential equations, perturbation methods
2010 Mathematics Subject Classification
C. Breiner was supported in part by NSF grant DMS-1308420 and by an AMS-Simons Travel Grant. S. J. Kleene was partially supported by NSF grant DMS-1004646.
Received 10 June 2014
Published 27 July 2018