Seminar talk, 23 December 2009

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Speaker: Arthemy Kiselev

Title: The spiral minimal surfaces and their Legendre and Weierstrass representations

Abstract:
Using a symmetry reduction, we construct a new class of spiral minimal surfaces that are invariant with respect to the composition of rotation and dilation of space, both centered at the origin. This reduction of the minimal surface equation leads to a cubic-nonlinear ordinary differential equation whose phase portrait yields an auxiliary Riccati's equation, and we apply the Ważewski topological principle for construction of its solutions. Then we establish the asymptotic behaviour of such spiral galaxy-like minimal surfaces. Also, we describe the exact solutions in parametric form using the Legendre and Weierstrass representations.

References:
A. Kiselev and V. Varlamov, The spiral minimal surfaces and their Legendre and Weierstrass representations, Differential Geom. Appl. 26 (2008), 23-41, doi:10.1016/j.difgeo.2007.11.039, local pdf.

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