International Scholarly Research Notices

Research Article

Minimal Surfaces with Only Horizontal Symmetries

Table 1

Symmetry I n v o l u t i o n 𝑧 - v a l u e s 𝑔 - v a l u e s
𝑆 𝐵 ( 𝑔 , 𝑧 ) → ( 𝑔 , − 𝑧 ) 𝑖 𝑡 , 0 < 𝑡 < 1 𝑔 ∈ ℝ +
𝐵 𝐿 ( 𝑔 , 𝑧 ) → ( − 𝑔 , 1 / 𝑧 ) 𝑒 𝑖 𝑡 , 𝜋 / 2 > 𝑡 > 0 𝑔 ∈ ℝ +
𝐿 𝑆 ( 𝑔 , 𝑧 ) → ( 𝑖 𝑔 , 𝑧 ) 𝑡 , 1 > 𝑡 > 0 𝑔 ∈ 𝑒 𝑖 𝜋 / 4 ℝ
𝑆 𝐵 ( 𝑔 , 𝑧 ) → ( 𝑔 , − 𝑧 ) 𝑖 𝑡 , 0 < 𝑡 < 1 𝑔 ∈ ℝ −
𝐵 𝐹 ( 𝑔 , 𝑧 ) → ( − 𝑔 , 1 / 𝑧 ) 𝑒 𝑖 𝑡 , 𝜋 / 2 > 𝑡 > 0 𝑔 ∈ ℝ −
𝐹 𝑆 ( 𝑔 , 𝑧 ) → ( − 𝑖 𝑔 , 𝑧 ) 𝑡 , 1 > 𝑡 > 0 𝑔 ∈ 𝑒 − 𝑖 𝜋 / 4 ℝ
𝜌 ℎ ( 𝑔 , 𝑧 ) → ( − 1 / 𝑔 , 𝑧 ) − 𝑥 , 𝑥 , 𝑥 − 1 , − 𝑥 − 1 𝑔 = ± 𝑖