title: Instability of a Möbius strip minimal surface and a link with systolic geometry.
abstract: We describe the first analytically tractable example of an instability of a nonorientable minimal surface under parametric variation of its boundary. A one-parameter family of incomplete Meeks Möbius surfaces is defined and shown to exhibit an instability threshold as the bounding curve is opened up from a double-covering of the circle. Numerical and analytical methods are used to determine the instability threshold by solution of the Jacobi equation on the double covering of the surface. The unstable eigenmode shows excellent qualitative agreement with that found experimentally for a closely related surface. A connection is proposed between systolic geometry and the instability by showing that the shortest noncontractable closed geodesic on the surface (the systolic curve) passes near the maximum of the unstable eigenmode.
authors: Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
authors: Adriana I
authors: AI
authors: Pesci
authors: Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
authors: Raymond E
authors: RE
authors: Goldstein
authors: Department of Physics and Centre for Complexity Science, University of Warwick, Coventry CV4 7AL, United Kingdom.
authors: Gareth P
authors: GP
authors: Alexander
authors: Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
authors: H Keith
authors: HK
authors: Moffatt