Randomized trial proves new theorems on bounded holomorphic functions, indicating strong properties at boundaries.
By the symmetrization method, new covering and distortion theorems are proved for holomorphic and bounded functions in a circular annulus that preserve one of its boundary components. In particular, inequalities including the Schwarzian derivative at a boundary point of the annulus are established. As corollaries, some differential inequalities for functions that are weakly univalent in the disk are presented. Unsolved problems are formulated.
No takes yet. Share an insight, caveat, or question.
V. Dubinin (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: