科研之友
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摘要
In 1957, Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2(n) translates of its interior. Up to now, this conjecture is still open for all n >= 3. In 1933, Borsuk made a conjecture that every n-dimensional bounded set can be divided into n + 1 subsets of smaller diameters. Up to now, this conjecture is open for 4 <= n <= 297. In this article we encode the two conjectures into continuous functions defined on the spaces of convex bodies, propose a four-step program to attack them, and obtain some partial results.
- 出版日期2010-9
- 单位北京大学
