Chain of Bifurcations for the Helicoid
Andrei Borisovich · AIP conference proceedings · 2008
In this paper the author studies the Plateau problem for a rectangular boundary contour lying on the helicoids surface that depends on some parameters. The contour is a sum of two axi‐symmetric spirals and two direct lines. The author finds out the critical values of parameters and proves the bifurcation theorem. The critical values are found by considering the linearised problem. The bifurcation parameter is a torsion frequency of helicoid (spirals). The nonlinear model is reduced to operator equation with Fredholm type operator of index 0. The Crandall‐Rabinowitz bifurcation theorem (gradient case) is used to prove the bifurcation theorem.