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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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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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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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Unstable minimal surface coboundaries
Acta Mathematica Sinica, 1986Let M be a compact oriented surface of type \((p,k)\), and \((N,h)\) a complete Riemannian manifold. If \(\mu\) is a conformal structure on M compatible with its orientation, then we write \((M,\mu)\) for the associated Riemann surface. The energy of a map \(\phi:(M,\mu) \to (N,h)\) from the Riemann surface to the Riemannian manifold is \[ (1.1)\quad E(
Chang, Kungching, Eells, James
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2007
Abstract We here review the theory of minimal surfaces, especially in 3-manifolds. Monotonicity properties of codimension one minimal surfaces, e.g. barrier surfaces, the maximum principle etc. complement the role of monotonicity in the theory of groups of homeomorphisms of 1-manifolds. When we come to study taut foliations in earnest in
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Abstract We here review the theory of minimal surfaces, especially in 3-manifolds. Monotonicity properties of codimension one minimal surfaces, e.g. barrier surfaces, the maximum principle etc. complement the role of monotonicity in the theory of groups of homeomorphisms of 1-manifolds. When we come to study taut foliations in earnest in
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International Journal of Theoretical Physics, 2006
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