3 problems

Let $\mu$ be the unique normalized invariant measure of a cubic critical homeomorphism of the circle, and let $HD(\mu)$ denote the Hausdorff dimension of its measure-theoretical su…

Minkowski's measure Nevai-class conjecture. The measure $\mu$ belongs to the Nevai class $N(\frac14,\frac12)$, equivalently its Jacobi coefficients have the limiting values…

Minkowski's measure regularity conjecture. Minkowski's measure $\mu$ is regular in the sense of Ullman--Stahl--Totik. This is a problem in logarithmic potential theory and orthogon…