The sharp local centering gap for symmetric decagons
Year: 2026
Type: preprint
Abstract: For origin-symmetric planar polygons with at most ten actual extreme vertices, the sharp local coefficient of the centering gap W(K)-V(K), normalized by the square of the Banach-Mazur distance excess from the affine-regular hexagon, is 1/4. The result is a provisional candidate conditional on the stated hexagon premises and identified local results. A labelled-vertex limit argument and full-body containment repair give the upper bound, including multiscale approaches. Genuine decagons provide the matching iterated-limit lower bound. With the earlier all-body sharpness result, twelve is the minimum polygon vertex count that can approach the all-body coefficient. No exact unrestricted minimum, effective neighborhood or complete extremizer classification is asserted.
Author: Barritz, Robert
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225467190