C∞-Convergence of Circle Patterns to Minimal Surfaces
2009 ◽
Vol 194
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pp. 149-167
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Keyword(s):
AbstractGiven a smooth minimal surface F: Ω → ℝ3 defined on a simply connected region Ω in the complex plane ℂ, there is a regular SG circle pattern . By the Weierstrass representation of F and the existence theorem of SG circle patterns, there exists an associated SG circle pattern in ℂ with the combinatoric of . Based on the relationship between the circle pattern and the corresponding discrete minimal surface F∊: → ℝ3 defined on the vertex set of the graph of , we show that there exists a family of discrete minimal surface Γ∊: → ℝ3, which converges in C∞(Ω) to the minimal surface F: Ω → ℝ3 as ∊ → 0.
1994 ◽
Vol 209
(1)
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1999 ◽
Vol 1999
(506)
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pp. 205-214
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2011 ◽
Vol 60
(1-4)
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pp. 311-323
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Keyword(s):
1983 ◽
Vol 6
(2)
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pp. 341-361
2019 ◽
Vol 2019
(753)
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pp. 159-191
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