Willmore曲面的點態估計之間隙

Abstract

吾人考慮3維球面上之Willmore 緊緻曲面。最近我們得到點態與保角類兩種估計。本計畫旨在探討該點態估計的間隙問題。吾人將分析四次微分形與Hopf二次微分形之關聯，因吾人認為此解析的四次微分形與估計問題密切相關。

Let M be a compact immersed Willmore surface in the 3-dimensional unit sphere. In our recent works, we obtain certain estimates in pointwise and conformal classes sense, respectively. One expects that there exists gap between different conformal classes. The purpose of this project is to find a pointwise gap estimate for certain Willmore surfaces. We also want to study connections between a holomorphic quartic differential and the Hopf differential because we believe that the property of the holomorphic quartic differential shall be close related to our desired estimate.