关于1-调和函数
On 1-Harmonic Functions
摘要：
常数1 $-tension field are given with applications in geometry via transformation group theory. In particular, we prove that every level hypersurface of such a subsolution is calibrated and hence is area-minimizing over $ \mathbb{R} $; and every 7-dimensional $ SO（2）\times SO（6）$-invariant absolutely area-minimizing integral current in $ \mathbb{R}^8 $ is real analytic. The assumption on the $ SO（2）\times SO（6）$-invariance cannot be removed, due to the first counter-example in $ \mathbb{R}^8 $的1-调和方程的整个子解的特征，由Bjereri，De Girogi和Giusti证明.
英文摘要：
Characterizations of entire subsolutions for the 1-harmonic equation of a constant 1$-tension field are given with applications in geometry via transformation group theory. In particular, we prove that every level hypersurface of such a subsolution is calibrated and hence is area-minimizing over $\mathbb{R}$; and every 7-dimensional $SO(2)\times SO(6)$-invariant absolutely area-minimizing integral current in $\mathbb{R}^8$ is real analytic. The assumption on the $SO(2) \times SO(6)$-invariance cannot be removed, due to the first counter-example in $\mathbb{R}^8$, proved by Bombieri, De Girogi and Giusti.
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