Inverted catenoids, curvature singularities and tethered membranes

Details Inverted catenoids, curvature singularities and tethered membranes Inverted catenoids, curvature singularities and tethered membranes

2007-02-14

arxiv.org/abs/cond-mat/0702322v1

Physics

Condensed Matter

Soft Condensed Matter

18 pages, 6 figures

Scientific paper

If a catenoid is inverted in any interior point, a deflated compact geometry is obtained which touches at two points (its poles). The catenoid is a minimal surface and, as such, is an equilibrium shape of a symmetric fluid membrane. The conformal symmetry of the Hamiltonian implies that inverted minimal surfaces are also equilibrium shapes. However, they exhibit curvature singularities at their poles. These singularities are associated with external forces pulling the poles together. Unlike the catenoid which is free of stress, there will be stress within the inverted shapes. If the surface area is fixed, reducing the external force induces a transition from a discocyte to a cup-shaped stomatocyte.

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