Chebyshev constant

Summary

The Chebyshev constant of a compact set $K$ in the plane measures how small a monic polynomial can be on $K$. For each degree $n$ one takes the least maximum of $\abs{p}$ on $K$ over monic polynomials $p$ of degree $n$. Then one takes its $n$-th root and lets $n$ tend to infinity. The extremal polynomials generalize the classical Chebyshev polynomials of an interval. A theorem of Fekete and Szegő says that the Chebyshev constant equals the logarithmic capacity of $K$.