论文标题
多边形空间中的面积二元性
Area-perimeter duality in polygon spaces
论文作者
论文摘要
考虑了两种自然叶子，以面积和周长为指导的平面多边形的配置空间，并详细研究其叶子的拓扑。特别是，确定同源组和同型叶片类型。还确定了具有固定面积和周长的多边形空间的同源组。此外，我们将经典的等值双重性扩展到所有关键点。总之，给出了多边形空间中双重极端问题的一些一般性评论。
Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type of leaves are determined. The homology groups of the spaces of polygons with fixed area and perimeter are also determined. Besides, we extend the classical isoperimetric duality to all critical points. In conclusion a few general remarks on dual extremal problems in polygon spaces and beyond are given.
