I-AIM Interdisciplinary Math Seminar
3:10 PM Friday Oct. 15 in SS5017A
"UNRECOGNIZED CLASSES OF MINIMAL SURFACES:
EXPONENTIAL FOAM AND GALAXY-LIKE SOLUTIONS"
Dr. A.V. Kiselev (Brock University)
Refreshments to follow in the adjacent Math Lounge
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"Unrecognized classes of minimal surfaces:
exponential foam and galaxy-like solutions."
Dr. Arthemy V. Kiselev of Brock University (joint work with Prof. V.I.Varlamov)
Abstract.
A symmetry reduction of the two-dimensional minimal area
surface equation leads to a cubic-nonlinear scalar dynamical system
on S^1. Its solutions propagate by logarithmic spirals intersecting
the circle and therefore define galaxy-like minimal surfaces in space.
Existence of a family of compactified phase trajectories that
correspond to tube-like spirals and an exponentially growing
self-intersecting foam is established. The resulting classes of minimal
surfaces are distinct from classical planes, helicoids, catenoids,
and Scherk's surfaces, hence their physical nature is unrecognized.
Reference.
[1] Kiselev A.V., Varlamov V.I.: A dynamical system associated with
classes of spiral galaxy-like minimal surfaces // Differential
Equations (2005), in preparation.
I-AIM Tea to follow in the adjacent Mathematics Lounge.
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