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Conformal mechanics of space curves
Jemal Guven
Any conformally invariant energy associated with a curve possesses tension-free equilibrium states which are self-similar. When this energy is the three dimensional conformal arc-l…
Conformal Mechanics of Planar Curves
Jemal Guven, Gregorio Manrique
Self-similar curves arise naturally as the tension-free equilibrium states of conformally invariant bending energies. The simplest example is the Möbius invariant conformal arc-len…
Conformal symmetry breaking and self-similar spirals
Jemal Guven
Self-similar curves are a recurring motif in nature. The tension-free stationary states of conformally invariant energies describe the simplest curves of this form. Planar logarith…
Isometric bending requires local constraints on free edges
Jemal Guven, Martin Michael Müller, Pablo Vázquez-Montejo
While the shape equations describing the equilibrium of an unstretchable thin sheet that is free to bend are known, the boundary conditions that supplement these equations on free…
Pinning of Diffusional Patterns by Non-Uniform Curvature
John R. Frank, Jemal Guven, Mehran Kardar +1
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patt…