Minimal sufaces foliated by circunferences / Superficies minimas folheadas por circunferencias
AUTOR(ES)
Lauriclecio Figueiredo Lopes
DATA DE PUBLICAÇÃO
2005
RESUMO
Minimal surfaces are known to be the ones with mean curvature zero. Classical exampIes are the catenoid, helicoid and the Scherk surface. Historically, they were associated with the property of minimizing area. However, they can even maximize it localIy for cases of normal variation which include the boundary. For fixed boundary, we shalI analyse when they realIy minimize the area functional. In the three-dimensional Euclidean space, the Weierstrass Representation Theorem expresses any minimal surface S by means of integraIs with a holomorphic and a meromorphic functions, usualIy denoted by f and g, respectively. The unitary normal N of S is fulIy determined by g. Concepts like "Gaussian curvature", "total curvature", "com pleteness" and "regularity" are also employed in order to read off some properties of minimal surfaces. Concerning the case for which the boundary of S consists of two disjoint circumferences, Enneper s and Shiffman s Theorems, The Schwarz s Reflection PrincipIe and the B6rling s Problem are fundamental tools to characterize the solutions, namely the catenoid and the Riemann s examples. AlI these are invariant by a reflectional symmetry in a plane, and also by a rotation of 180-degree around a straight line. The symmetric Weierstrass-Pfunction is very useful to deduce these properties.
ASSUNTO(S)
minimal surfaces differential geometry riemann geometria diferencial superificies minimas superficies riemann surfaces
