| 刘进.$F$-Willmore曲面的间隙现象[J].数学年刊A辑,2014,35(3):333~350 |
| $F$-Willmore曲面的间隙现象 |
| Gap Phenomenon of F-Willmore Surfaces |
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| DOI： |
| 中文关键词: Willmore猜想, $F$-Willmore曲面, Simons类积分不等式 |
| 英文关键词:Willmore conjecture, $F$-Willmore surface, Simons' type inequality |
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| 中文摘要: |
| 对于空间形式中的2维曲面, 定义了$F$-Willmore泛函, 此泛函包括经典的Willmore泛函作为特殊情形. $F$-Willmore泛函的临界点称为$F$-Willmore曲面.
推导了第 1 变分公式并由此构造了$F$-Willmore曲面的典型例子. 利用自伴算子作用于特殊的实验函数, 得到了Simons类积分不等式, 讨论了$F$-Willmore曲面的间隙现象, 定出了间隙端点对应的特殊曲面. |
| 英文摘要: |
| For a $2$-dimensional surface in space forms, an $F$-Willmore functional is constructed,
which includes and generalizes the well-known classic Willmore functional of surface.
The critical point of $F$-Willmore is called $F$-Willmore surface, for which the variational equation and the Simons' type
integral inequality are obtained. Moreover, for some particular functions $F$,
the author constructs examples of $F$-Willmore surface and gives a characterization of $F$-Willmore tori and Veronese surface by use of Simons' type integral inequality. |
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