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Quasicrystalline minimal surfaces
Physical Review B, 1994Minimal surfaces are considered as alternatives to tilings in the search for simple mathematical objects that have the properties of a quasicrystal. The construction of such objects, it seems, has not been addressed before and we propose a solution in the form of a limiting process.
, Sheng, , Elser
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The Quarterly Journal of Mathematics, 2001
In this work, infinitely many families of rational minimal surfaces in Euclidean 3-space are constructed. A rational minimal surface is a complete conformal non-planar minimal immersion whose Weierstrass representation is defined on the Riemann 2-sphere punctured at finitely many points (the puncture points are mapped by the Weierstrass representation ...
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In this work, infinitely many families of rational minimal surfaces in Euclidean 3-space are constructed. A rational minimal surface is a complete conformal non-planar minimal immersion whose Weierstrass representation is defined on the Riemann 2-sphere punctured at finitely many points (the puncture points are mapped by the Weierstrass representation ...
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International Journal of Theoretical Physics, 2006
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Applied Optics, 1969
It has been pointed out that the meridional object and image foci as well as the meridional center of curvature will lie on the same straight line if the condition Delta (n cos(2)i/t) = Delta (n/t) is satisfied. The surfaces fulfilling this condition do not introduce astigmatism; hence they have been called minimal astigmatism surfaces. The generalized
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It has been pointed out that the meridional object and image foci as well as the meridional center of curvature will lie on the same straight line if the condition Delta (n cos(2)i/t) = Delta (n/t) is satisfied. The surfaces fulfilling this condition do not introduce astigmatism; hence they have been called minimal astigmatism surfaces. The generalized
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Minimal Surfaces and Sobolev Gradients
SIAM Journal on Scientific Computing, 1995The authors treat the problem of computing triangle-based piecewise linear approximations to parametric minimal surfaces in the Euclidean 3-space. They employ the Sobolev metric method to descend the surface-area functional at each iteration. Test results show that, starting with extremely poor initial estimates, a few descent iterations produce ...
Robert J. Renka, J. W. Neuberger
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, 1993 This book contains recent results from a group focusing on minimal surfaces in the Moscow State University seminar on modern geometrical methods, headed by A. V. Bolsinov, A. T. Fomenko, and V. V. Trofimov. The papers collected here fall into three areas:
Fomenko, A T
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Annals of Global Analysis and Geometry, 2001
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2023
Minimal surfaces are an object within differential geometry. Differential geometry is a field of mathematics which studies geometric objects that can be described by smooth, i.e. infinitely differentiable maps. These geometric objects are called manifolds.
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Minimal surfaces are an object within differential geometry. Differential geometry is a field of mathematics which studies geometric objects that can be described by smooth, i.e. infinitely differentiable maps. These geometric objects are called manifolds.
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Minimal Surfaces with Free Boundaries and Unstable Minimal Surfaces
1950In this chapter we shall discuss two extensions of the theory of minimal surfaces. First we shall solve the problem of finding minimal surfaces of least area when the whole boundary or part of it is not prescribed but left free on given manifolds.1 Secondly we shall study minimal surfaces whose areas are not relative minima.
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