Validity of the Strong Version of the Union of Uniform Closed Balls Conjecture in the Plane
Chadi Nour, Jean Takche
TL;DR
This paper proves the strong version of a longstanding geometric conjecture about the union of uniform closed balls in the plane, confirming its validity.
Contribution
It provides a proof for the strong version of the union of uniform closed balls conjecture in the plane, a problem posed in 2011.
Findings
The strong version of the conjecture is valid in the plane.
The proof confirms the conjecture's correctness for planar cases.
This advances understanding of geometric covering problems.
Abstract
We prove the validity of the strong version of the union of uniform closed balls conjecture, formulated in 2011 as [4, Conjecture 2.5], in the plane.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Meromorphic and Entire Functions