We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space, and every viscosity mean convex cone admits a properly embedded smooth mean convex self-expander asymptotic to it near infinity. These two together confirm a conjecture of Lawson (Geom. Meas. Theor. Calcu. Var. 44:441, 1986, Problem 5.7).

中文翻译：

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平均凸锥的平均凸平滑

我们证明，任何最小化超锥都可以被扰动到欧几里得空间中正确嵌入的平滑最小化超曲面的一侧，并且每个粘性平均凸锥都允许一个正确嵌入的平滑平均凸自展开器渐近到接近无穷大。这两者共同证实了劳森的猜想（Geom. Meas. Theor. Calcu. Var. 44:441, 1986, Problem 5.7）。