The Global Theory of Minimal Surfaces in Flat Spaces: Lectures Given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in Martina Franca, Italy, June 7-14, 1999, Issue 1775In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space. |
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The Global Theory of Minimal Surfaces in Flat Spaces: Lectures ..., Issue 1775 W.H. III Meeks,A. Ros,H. Rosenberg No preview available - 2002 |
The Global Theory of Minimal Surfaces in Flat Spaces: Lectures given at the ... W.H. III Meeks,A. Ros,H. Rosenberg No preview available - 2014 |
Common terms and phrases
3-manifold annular end annulus asymptotic boundary components bounded Bryant surfaces catenoid catenoid cousin end compact complete minimal surface constant contradiction converges Corollary denote disjoint disk E₁ embedded minimal surface embedded surface equation Euclidean exists finite number finite topology finite total curvature flat 3-manifold function Gauss map Gaussian curvature genus genus zero geodesic Geometry graph Halfspace helicoidal holomorphic homothety horizontal horosphere implies integer intersection Lemma M₁ Math maximum principle mean convex mean curvature meromorphic metric Mn}n moduli space nonflat normal vector number of ends orientable p₁ periodic minimal surfaces planar ends Plateau problem principle at infinity Proof properly embedded Bryant properly embedded minimal properly immersed proved radius Riemann second fundamental form singly periodic space surface in R3 surface with finite tangent plane Theorem Theory vertical forces VIII W. H. Meeks
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Page 110 - The geometry and conformai structure of properly embedded minimal surfaces of finite topology in R 3 ; Invent. Math. 114