کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4614616 | 1339294 | 2016 | 17 صفحه PDF | دانلود رایگان |
In this work we study subdivisions of k-rotationally symmetric planar convex bodies that minimize the maximum relative diameter functional. For some particular subdivisions called k-partitions, consisting of k curves meeting in an interior vertex, we prove that the so-called standard k-partition (given by k equiangular inradius segments) is minimizing for any k∈Nk∈N, k⩾3k⩾3. For general subdivisions, we show that the previous result only holds for k⩽6k⩽6. We also study the optimal set for this problem, obtaining that for each k∈Nk∈N, k⩾3k⩾3, it consists of the intersection of the unit circle with the corresponding regular k-gon of certain area. Finally, we also discuss the problem for planar convex sets and large values of k, and conjecture the optimal k-subdivision in this case.
Journal: Journal of Mathematical Analysis and Applications - Volume 435, Issue 1, 1 March 2016, Pages 718–734