2026/07/21 by Siarhei Finski
#math.CV #math.AG #math.CA #math.FA
By Montel's theorem, the continuous functions on a compact subset of a complex manifold that admit uniformly bounded holomorphic extensions to the manifold form a compact set in the uniform topology. We render this compactness quantitative by determining the asymptotics of the associated metric entropy, thereby giving a new solution to a problem of Kolmogorov for domains in ℂn and extending the solution to domains in arbitrary Stein manifolds.