The cone over the Clifford torus in R4 isΦ-minimizing
The cone over the Clifford torus in R4 isΦ-minimizing
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R4 中 Clifford 环面上的锥体是 Φ 最小化
DOI：
10.1007/bf01446576
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发表时间：
1991
影响因子：
1.4
通讯作者：
F. Morgan
中科院分区：
文献类型：
--
作者：
F. Morgan
本文如[M4]所述，证明了面积极小化超曲面（积分流）的正则性结果不适用于极小化所有其它椭圆被积函数的积分的超曲面。特别地，我们给出了R4中的一个奇异三维O-极小化超曲面。该示例示出了Almgren、Schoen和Simon [AlmSS，定理II. 7]，这保证了通过R3的规律性。曲面是Clifford环面S 1 x S 1CR 2 x R2上的圆锥C：
This paper shows as announced in [M4] that the regularity results for areaminimizing hypersurfaces (integral currents) do not hold for hypersurfaces minimizing the integrals of all other elliptic integrands~. In particular, we give a singular 3-dimensional O-minimizing hypersurface in R 4. This example shows the sharpness of the results of Almgren, Schoen, and Simon [AlmSS, Theorem II. 7], which guarantee regularity up through R 3. The surface is the cone C over the Clifford torus S 1 x S 1CR2x R2: