Resumen de Linearization and explicit solutions of the minimal surface equation

Alexander G. Reznikov

• 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.