Asymptotics of Chebyshev Polynomials, III. Sets Saturating Szeg\H{O}, Schiefermayr, and Totik--Widom Bounds

We determine which sets saturate the Szeg}o and Schiefermayr lower bounds on the norms of Chebyshev Polynomials. We also discuss sets that saturate the Totik–Widom upper bound.