On the perimeter of k pairwise disjoint convex bodies contained in a convex set in the plane
نویسنده
چکیده
We prove the following isoperimetric inequality in R, conjectured by Glazyrin and Morić. Given a convex body S and k pairwise disjoint convex bodies C1, . . . , Ck that are contained in S, then ∑k i=1 Per(Ci) ≤ Per(S) + 2(k − 1)Diam(S). Here Per(·) denotes the perimeter of a set and Diam(·) is the diameter of a set.
منابع مشابه
Equipartitioning by a convex 3-fan
We show that for a given planar convex set K of positive area there exist three pairwise internally disjoint convex sets whose union is K such that they have equal area and equal perimeter. © 2009 Elsevier Inc. All rights reserved.
متن کاملA convex combinatorial property of compact sets in the plane and its roots in lattice theory
K. Adaricheva and M. Bolat have recently proved that if $,mathcal U_0$ and $,mathcal U_1$ are circles in a triangle with vertices $A_0,A_1,A_2$, then there exist $jin {0,1,2}$ and $kin{0,1}$ such that $,mathcal U_{1-k}$ is included in the convex hull of $,mathcal U_kcup({A_0,A_1, A_2}setminus{A_j})$. One could say disks instead of circles.Here we prove the existence of such a $j$ and $k$ ...
متن کاملBundling Three Convex Polygons to Minimize Area or Perimeter
Given a set P = {P0, . . . , Pk−1} of k convex polygons having n vertices in total in the plane, we consider the problem of finding k translations τ0, . . . , τk−1 of P0, . . . , Pk−1 such that the translated copies τiPi are pairwise disjoint and the area or the perimeter of the convex hull of ⋃k−1 i=0 τiPi is minimized. When k = 2, the problem can be solved in linear time but no previous work ...
متن کاملNew Results on Stabbing Segments with a Polygon
We consider a natural variation of the concept of stabbing a set of segments with a simple polygon: a segment s is stabbed by a simple polygon P if at least one endpoint of s is contained in P, and a segment set S is stabbed by P if P stabs every element of S. Given a segment set S, we study the problem of finding a simple polygon P stabbing S in a way that some measure of P (such as area or pe...
متن کاملSweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Combinatorica
دوره 37 شماره
صفحات -
تاریخ انتشار 2017