Year: 2026
Type: preprint
Abstract: We establish a least-squares lower bound for the logarithmic capacity of an arbitrary compact plane set, extending an inequality previously known for connected sets. The bound generalizes classical inequalities involving area and moment of inertia. It is sharp for disks, and asymptotically sharp for compact sets whose capacity coincides with that of their interior. We further show that asymptotic sharpness holds for general compact sets if we replace logarithmic capacity by minimal carrier capacity.
Source: arXiv (Cornell University)
Author: Ransford, Thomas
Institution: Université Laval
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1119843451
OpenAlex ID: W7223027926