Text S1: Membrane Energy Minimization
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چکیده
Assuming axial symmetry, we introduce a surface of revolution approach to model the membrane at equilibrium. We consider a generating curve γ parameterized by arc length s lying in the x− z plane. The curve γ is expressed as γ(0, s1) → R γ(s) = (R(s), 0, z(s)) (S1.1) where s1 is the total arc-length. This generating curve leads to a global parametrization of the membrane expressed as X : (0, s1)× (0, 2π) → R 3 (S1.2) X(s, u) = (R(s)cos(u), R(s)sin(u), z(s)) (S1.3) where u is the angle of rotation about z-axis. With this parametrization, the mean curvature H and the Gaussian curvature K are given as follows respectively
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