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| 摘要: |
| 本文研究了Möbius几何中的Pinching问题,利用极小模张量原理在单位球空间的Möbius迷向超曲面上, Möbius第二基本形式的二次梯度模平方进行估计,得到了一个有用的不等式,并利用这个公式等到了关于Blaschke张量特征值的一个拼挤定理. |
| 关键词: 极小模张量 Möbius第二基本形式 超曲面 |
| DOI： |
| 分类号:O186.16 |
| 基金项目: |
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| APPLICATION OF THE MINIMAL NORM TENSOR PRINCIPLE IN Möbius GEOMETRY |
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XING Jin-xiong,GONG Yi-fan
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| Abstract: |
| This paper addresses Pinching problems in Möbius geometry for hypersurfaces with Möbius isotropy in the unit sphere. By implementing the minimum norm tensor principle, we rigorously estimate the squared norm of the quadratic gradient term associated with the Möbius second fundamental form. This analysis yields a critical inequality governing the geometric configuration. Leveraging this inequality, we subsequently prove a Pinching theorem characterizing the eigenvalues of the Blaschke tensor. |
| Key words: minimal norm tensor Möbius second fundamental form hypersurface |
