A duality result between the minimal surface equation and the maximal surface equation

Citation
Lj. Alias et B. Palmer, A duality result between the minimal surface equation and the maximal surface equation, AN AC BRASI, 73(2), 2001, pp. 161-164
Citations number
2
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Multidisciplinary
Journal title
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS
ISSN journal
0001-3765 → ACNP
Volume
73
Issue
2
Year of publication
2001
Pages
161 - 164
Database
ISI
SICI code
0001-3765(200106)73:2<161:ADRBTM>2.0.ZU;2-9
Abstract
In this note we show how classical Bernstein's theorem on minimal surfaces in the Euclidean space can be seen as a consequence of Calabi-Bernstein's t heorem on maximal surfaces in the Lorentz-Minkowski space (and viceversa). This follows from a simple but nice duality between solutions to their corr esponding differential equations.