二维Brunn-Minkowski不等式中的近似等式
Near equality in the two-dimensional Brunn-Minkowski inequality
摘要：
如果二维欧几里得空间的一对子集在Brunn-Minkowski不等式中几乎相等，在这个意义上，相关和集的测度几乎等于不等式提供的下界，那么这些集合必须与一对位似凸集几乎重合。证明依赖于一个连续模拟的定理弗赖曼的特点有限集的整数的总和几乎是最小的大小。本草案作了一些小的更正和澄清。
英文摘要：
If a pair of subsets of two-dimensional Euclidean space nearly achieves equality in the Brunn-Minkowski inequality, in the sense that the measure of the associated sumset is nearly equal to the lower bound provided by the inequality, then these sets must nearly coincide with a pair of homothetic convex sets. The proof relies on a continuum analogue of a theorem of Freiman which characterizes finite sets of integers whose sumsets are of nearly minimal size. Small corrections and clarifications have been made in this draft.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
