关于Clifford环面在给定等周比下的唯一性
On the Uniqueness of Clifford Torus with Prescribed Isoperimetric Ratio
摘要：
Marques-Neves定理断言在所有环面（即亏格1）闭曲面中，Clifford环面具有最小的Willmore能量$\int H^2 \, dA$。由于Willmore能量是不变的M{<$}bius变换，因此可以证明存在一个单参数族，直到同素性，亏格为1的Willmore极小元。这是一个自然的猜想，这样的极小是唯一的，如果规定其等周比。在这篇文章中，我们表明，这个猜想可以减少到一个多项式递归的正性问题。
英文摘要：
The Marques-Neves theorem asserts that among all the torodial (i.e. genus 1) closed surfaces, the Clifford torus has the minimal Willmore energy $\int H^2 \, dA$. % It is a natural conjecture that if one prescribes the isoperimetric Since the Willmore energy is invariant M{ö}bius transformations, it can be shown that there is a one-parameter family, up to homotheties, of genus 1 Willmore minimizers. It is then a natural conjecture that such a minimizer is unique if one prescribes its isoperimetric ratio. In this article, we show that this conjecture can be reduced to the positivity question of a polynomial recurrence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
