Year: 2026
Type: preprint
Abstract: We consider the isoperimetric problem with planar density equal to 1 on a horizontal strip and to a constant $λ>1$ outside the strip. We resolve a conjecture made by Cañete-Miranda Jr-Vittone by showing that every four-arc region admits a three-arc competitor with the same weighted area and strictly smaller weighted perimeter. The argument applies to every $λ>1$ and gives an explicit positive lower bound for the perimeter difference.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214965804