内接正方形与关系回避路径
Inscribed Squares and Relation Avoiding Paths
摘要：
我们开发了一个连接的内接广场问题和问题的理解关系避免路径在一个复杂的向量空间。我们的主要定理是，没有内接正方形的乔丹曲线将具有一个看似不可能的结构，我们称之为正方形包络。我们将对向量空间中关系回避路的性质作一些说明，并证明这些说明将暗示具有许多任意复杂奇点的Jordan曲线中存在内接正方形。
英文摘要：
We develop a connection between the inscribed square problem and the question of understanding relation avoiding paths in a complex vector space. Our main theorem is that a Jordan curve with no inscribed squares would have a seemingly impossible structure which we call a square envelope. We will make some conjectures about the nature of relation avoiding paths in vector spaces, and show that these conjectures would imply the existence of inscribed squares in Jordan curves with finitely many arbitrarily complicated singularities.
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