论文标题
关于克利福德圆环的独特性，有规定的等值比
On the Uniqueness of Clifford Torus with Prescribed Isoperimetric Ratio
论文作者
论文摘要
Marques-neves定理断言，在所有圆环（即属1）中，封闭的表面，克利福德圆环的willmore Energy $ \ int H^2 \，da $。 ％自然的猜想是，如果一个人开处方等法，因为willmore能量是不变的m {Ö} bius变换，则可以证明有一个单参数家族，直到同型属，属于属1 willmore minimizizer属。这样自然的猜想是，如果一个人规定其等速度比率，那么这种最小化是唯一的。在本文中，我们表明，这种猜想可以简化为多项式复发的积极问题。
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.
