近似j维Koch型集是潜极小曲面
Approximately j-dimensional Koch type sets are potentially minimal surfaces
摘要：
本文研究了Simon提出的极小曲面的奇异集的近似j维性质。这导致了约j维曲面的8个变化的分类方面的尺寸和局部有限Hausdorff措施。我们表明，奇点集必须要么表现良好，或基本上纯粹不可求长。构造和推广了可能发生的不可求积集的例子。它们被证明是伪分形的，并与著名的Koch集有关。各种表示的措施和尺寸的集，以及一个很好的平衡，螺旋性质的集。
英文摘要：
We investigate the approximate j-dimensionality of the singularity sets of minimal surfaces prescribed by Simon. This leads to the clasification of 8 variations of approximately j-dimensional surfacs in terms of dimension and locally finite Hausdorff measure. We show that the singularity sets must either be well behaved or essentially purely unrectifiable. Examples of the unrectifiable sets that could occur are constructed and generalised. They are shown to be pseudo-fractal and related to the well known Koch Sets. Various representations of the measure and dimension of the sets are shown, as well as a fine balance in the spiralling nature of the sets.
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