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

Anais da Academia Brasileira de Ciências

Luis J. AlÍas²  Bennett Palmer¹ 

[1] ,Universidad de Murcia Departamento de Matemáticas Murcia,Spain

关键词: Minimal surface equation;    Maximal surface equation;    Bernstein's theorem;    Calabi-Bernstein's theorem;    Equações de superfícies mínimas;    Equações de superfícies máximas;    teorema de Bernstein;    teorema de Calabi-Bernstein;   

DOI  :  10.1590/S0001-37652001000200002

来源: SciELO

【 摘 要 】

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 theorem on maximal surfaces in the Lorentz-Minkowski space (and viceversa). This follows from a simple but nice duality between solutions to their corresponding differential equations.

【 授权许可】

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