论文标题
四维Willmore型Hypersurfaces的规律性
Regularity of four dimensional Willmore-type hypersurfaces
论文作者
论文摘要
研究了四维形式不变的能量。这种能量概括了众所周知的二维Willmore Energy。尽管不是积极的确定性，但它包括最小的超曲面作为临界点。我们计算出其第一个变化，并通过将Noether定理应用于不变性，我们得出了一些保护定律，这些定律被其关键点和良好的分析处置所满足。特别是，我们表明其关键点很顺利。我们还研究了威尔莫尔能量的其他可能的四维概括，并提供了有力的证据，表明这种能量的关键点不包括最小的超曲面。
A four dimensional conformally invariant energy is studied. This energy generalises the well known two-dimensional Willmore energy. Although not positive definite, it includes minimal hypersurfaces as critical points. We compute its first variation and by applying the Noether theorem to the invariances, we derive some conservation laws which are satisfied by its critical points and with good analytical dispositions. In particular, we show that its critical points are smooth. We also investigate other possible four dimensional generalisations of the Willmore energy, and give strong evidence that critical points of such energies do not include minimal hypersurfaces.
