Linearization and explicit solutions of the minimal surface equations.

Reznikov, Alexander G.. "Linearization and explicit solutions of the minimal surface equations.." Publicacions Matemàtiques 36.1 (1992): 39-46. <http://eudml.org/doc/41170>.

@article{Reznikov1992,
abstract = {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.},
author = {Reznikov, Alexander G.},
journal = {Publicacions Matemàtiques},
keywords = {Hipersuperficies; Superficies minimales; Ecuaciones lineales; Soluciones; support functions},
language = {eng},
number = {1},
pages = {39-46},
title = {Linearization and explicit solutions of the minimal surface equations.},
url = {http://eudml.org/doc/41170},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Reznikov, Alexander G.
TI - Linearization and explicit solutions of the minimal surface equations.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 1
SP - 39
EP - 46
AB - 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.
LA - eng
KW - Hipersuperficies; Superficies minimales; Ecuaciones lineales; Soluciones; support functions
UR - http://eudml.org/doc/41170
ER -