We show that the apparatus of support functions, usually used in convex surfaces theory, leads to the linear equation Δh + 2h = 0 describing locally germs of minimal surfaces. Here Δ 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 Δ h + 2h = 0 becomes inequality wherever the Gauss curvature of a minimal hypersurface is nonzero.
@article{urn:eudml:doc:41170,
title = {Linearization and explicit solutions of the minimal surface equations.},
journal = {Publicacions Matem\`atiques},
volume = {36},
year = {1992},
pages = {39-46},
zbl = {0773.53004},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41170}
}
Reznikov, Alexander G. Linearization and explicit solutions of the minimal surface equations.. Publicacions Matemàtiques, Tome 36 (1992) pp. 39-46. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41170/