科研之友
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摘要
We present a two- parameter family of minimal surfaces constructed by lifting a family of planar harmonic mappings. In the process, we use the Clunie and Sheil- Small shear construction for planar harmonic mappings convex in one direction. This family of minimal surfaces, through a continuous transformation, has connections with three well- known surfaces: Enneper%26apos;s surface, the wavy plane, and the helicoid. Moreover, the identification process used to recognize the surfaces provides a connection to surfaces that give tight bounds on curvature estimates first studied in a 1988 work by Hengartner and Schober.
- 出版日期2014
