Linearization and explicit solutions of the minimal surface equation

• Autores: Alexander G. Reznikov
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 36, Nº 1, 1992, págs. 39-46
• Idioma: inglés
• Títulos paralelos:
  • Linealización y soluciones explícitas de la ecuación de superficies mínimas
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• Resumen

  • We show that the apparatus of support functions, usually used in convex surfaces theory, leads to the linear equation ?h + 2h = 0 describing locally germs of minimal surfaces. Here ? is the Laplace-Beltrami operator on the standard two-dimensional sphere. It explains the existence of the sum operator of minimal surfaces, introduced recently. In 4-dimensional space the equation ? h + 2h = 0 becomes inequality wherever the Gauss curvature of a minimal hypersurface is nonzero.