Journal ArticleDOI
Minimal surfaces based on the catenoid
David Hoffman,William H. Meeks +1 more
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Hoffman as discussed by the authors was the 1990 winner of the MAA Chauvenet Prize for Mathematical Programming. But he was not the winner of this prize in the 1990s.Abstract:
DAVID HOFFMAN is Professor of Mathematics and Co-Director of the Geometry, Analysis, Numerics and Graphics Center (GANG) at the University of Massachusetts, Amherst. He earned his Ph.D. in mathematics at Stanford, after receiving undergraduate degrees at the University of Rochester (in history and mathematics). He has pursued research and/or teaching at the Universities of Durham and Warwick (UK), Michigan and Stanford, as well as IMPA (Rio de Janeiro, Brazil) and the University of Paris VII. He is the 1990 recipient of the MAA Chauvenet Prize.read more
Citations
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Journal ArticleDOI
Complete embedded minimal surfaces of finite total curvature
TL;DR: A general construction for complete embedded minimal surfaces of nite total curvature in Euclidean three space is carried out in this paper, in particular ex amples with an arbitrary number of ends are given for the first time.
Journal ArticleDOI
The classical theory of minimal surfaces
William H. Meeks,Joaquín Pérez +1 more
TL;DR: A survey of recent spectacular successes in minimal surface theory can be found in this article, where it is shown that the plane, the helicoid, the catenoid and the one-parameter family fRtgt2(0;1) of Riemann minimal examples are the only complete, properly embedded, minimal planar domains in R 3.
Book
Geometry from a differentiable viewpoint
TL;DR: In this paper, the authors introduce differential geometry and the history of the parallel postulate in Euclidean and non-Euclidean geodesic geometry, and introduce the notion of space-time manifolds.
MonographDOI
A Survey on Classical Minimal Surface Theory
William H. Meeks,Joaquín Pérez +1 more
TL;DR: Meeks and Perez as discussed by the authors present a survey of recent spectacular successes in classical minimal surface theory, focusing on the classification of minimal planar domains in three-dimensional Euclidean space.
MonographDOI
The Mathematics of Soap Films: Explorations with Maple®
TL;DR: The mathematics of soap films The calculus of variations and shape Maple, soap films and minimal surfaces Bibliography Index as mentioned in this paper is a good starting point for a quick trip through differential geometry and complex variables.
References
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BookDOI
Gesammelte mathematische Abhandlungen
TL;DR: Weierstrass et al. as discussed by the authors presented an algebraic model of the Minimalflache, which was used for the analysis of the Variationsrechnung.
Journal ArticleDOI
The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
TL;DR: In this paper, it was shown that stable minimal surfaces in Riemannian 3-manifolds can be expressed analytically by the condition that o n any compact domain of M, the first eigenvalue of the operator A+Ric(v)+AI* be positive.
Journal ArticleDOI
Equilibrium bicontinuous structure
TL;DR: A bicontinuous structure is a bicountinuous partitioning in which each subvolume is filled with a distinct, not necessarily uniform composition or state of matter.