A Cusp Singularity in Surfaces That Minimize an Anisotropic Surface Energy

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Science  01 Aug 1986:
Vol. 233, Issue 4763, pp. 548-551
DOI: 10.1126/science.233.4763.548


A mathematical proof shows that a surface with a cusp-shaped singularity can arise from minimizing an anisotropic surface free energy for a portion of a crystal surface. Such cusps have been seen on crystal surfaces but usually have been interpreted as being the result of defects or nonequilibrium crystal growth. Our result predicts that they can occur as equilibrium or near-equilibrium phenomena. It also enriches the mathematical theory of minimal surfaces.