Add to ORKGFor a given planar convex compact set K, consider a bisection {A,B} of K (i.e., A [ B = K and whose common boundary A \ B is an injective continuous curve connecting two boundary points of K) minimizing the corresponding maximum diameter (or maximum width) of the regions among all such bisections of K. In this note we study some properties of these minimizing bisections and we provide analogous to the isodiametric (Bieberbach, 1915), the isominwidth (P´al, 1921), the reverse isodiametric (Behrend, 1937), and the reverse isominwidth (Gonz´alez Merino & Schymura, 2018) inequalities.Ministerio de Economía y Competitividad MTM2017-84851-C2-1-PJunta de Andalucía FQM-32
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AbstractWe find the largest ϵ (approximately 1.71579) for which any simple closed path α in the univ...
Abstract. We give a sharp lower bound on the area of a domain that can be enclosed by a closed embed...
As it is well-known, the classical isoperimetric problem on the plane claims to find a simple closur...
In this paper we study the bisections of a centrally symmetric planar convex body which minimize the...
Fencing problems deal with the bisection of a convex body in a way that some geometric measures are ...
We consider subdivisions of convex bodies G in two subsets E and G\E. We obtain several inequalities...
In this paper, we study the bisections of a centrally symmetric planar convex body which minimize th...
In this paper we study the following quantitative isoperimetric inequality in the plane: $\lambda_0^...
Abstract. We consider subdivisions of bounded convex sets G in two subsets E and G \ E. We obtain se...
What is the most efficient way to fence land when you’ve only got so many metres of fence? Or, to pu...
In this work we study subdivisions of k-rotationally symmetric planar convex bodies that minimize t...
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The Isoperimetric Inequality has many different proofs using methods from diverse mathematical field...
Abstract. A four part dissection and rearrangement provides a new proof of the isoperimetric inequal...
Inspired by a planar partitioning problem involving multiple improper chambers, this article investi...
AbstractWe find the largest ϵ (approximately 1.71579) for which any simple closed path α in the univ...
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