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Helicoidal minimal surfaces of prescribed genus
Acta Mathematica ( IF 3.7 ) Pub Date : 2016-01-01 , DOI: 10.1007/s11511-016-0139-z
David Hoffman , Martin Traizet , Brian White

For every genus g, we prove that $${\mathbf{S}^2\times\mathbf{R}}$$S2×R contains complete, properly embedded, genus-g minimal surfaces whose two ends are asymptotic to helicoids of any prescribed pitch. We also show that as the radius of the $${\mathbf{S}^2}$$S2 tends to infinity, these examples converge smoothly to complete, properly embedded minimal surfaces in $${\mathbf{R}^3}$$R3 that are helicoidal at infinity. We prove that helicoidal surfaces in $${\mathbf{R}^3}$$R3 of every prescribed genus occur as such limits of examples in $${\mathbf{S}^2\times\mathbf{R}}$$S2×R.

中文翻译:

规定属的螺旋最小表面

对于每个属 g,我们证明 $${\mathbf{S}^2\times\mathbf{R}}$$S2×R 包含完整的、正确嵌入的、 gen-g 最小曲面,其两端渐近于任何规定的间距。我们还表明,随着 $${\mathbf{S}^2}$$S2 的半径趋向于无穷大,这些例子平滑地收敛到完整的、正确嵌入的最小曲面 $${\mathbf{R}^3} $$R3 在无穷远处呈螺旋状。我们证明每个指定属的 $${\mathbf{R}^3}$$R3 中的螺旋面作为 $${\mathbf{S}^2\times\mathbf{R}}$ 中的示例限制出现$S2×R。
更新日期:2016-01-01
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