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math.DG2024
Isoperimetric Ratios of Toroidal Dupin Cyclides
Alin Bostan, Thomas Yu, Sergey Yurkevich
The combination of recent results due to Yu and Chen [Proc. AMS 150(4), 2020, 1749-1765] and to Bostan and Yurkevich [Proc. AMS 150(5), 2022, 2131-2136] shows that the 3-D Euclidea…
math.DG2020
On the Uniqueness of Clifford Torus with Prescribed Isoperimetric Ratio
Thomas Yu, Jingmin Chen
The Marques-Neves theorem asserts that among all the torodial (i.e. genus 1) closed surfaces, the Clifford torus has the minimal Willmore energy . % It is a natural…