Peter A. Djondjorov

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An interesting class of axially symmetric surfaces, which generalizes Delaunay's unduloids and provides solutions of the shape equation is described in explicit parametric form. This class provide the first analytical examples of surfaces with periodic curvatures studied by K. Kenmotsu and leads to some unexpected relationships among Jacobian elliptic(More)
The consideration of some non-standard parametric Lagrangian leads to a fictitious dynamical system which turns out to be equivalent to the Euler problem for finding out all possible shapes of the lamina. Integrating the respective differential equations one arrives at novel explicit parameteri-zations of the Euler's elastica curves. The geometry of the(More)
This study is concerned with the determination of the mechanical behaviour of closed fluid lipid bilayer membranes (vesicles) under a uniform hydrostatic pressure, pressed against and adhering onto a flat homogeneous rigid substrate. Assuming that the initial and deformed shapes of the vesicle are axisymmetric, a variational statement of the problem is(More)
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