A Schwarz-type formula for minimal surfaces in Euclidean space Rn

✍ Scribed by Luis J Alı́as; Pablo Mira

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 75 KB
• Volume: 334
• Category: Article
• ISSN: 1631-073X
• DOI: 10.1016/s1631-073x(02)02280-x

✦ Synopsis

This paper introduces a complex representation for minimal surfaces in R n , based on the Schwarz formula which solves the classical Björling problem for minimal surfaces in R 3 . As an application, it is shown that a k-dimensional plane of R n is a plane of symmetry of a minimal surface in R n provided it intersects the surface orthogonally. A procedure for the construction of minimal surfaces is also described. This procedure introduces minimal surfaces with prescribed geometric properties, starting from real analytic curves in R n .