Transversal Hölder Criteria and Dini--Zygmund Endpoint Regularity for Hyperbolic Harmonic Mappings
Year: 2026
Type: preprint
Abstract: Let $n\ge3$, and let $u$ be a bounded hyperbolic harmonic mapping on the real hyperbolic upper half-space $\mathbb H^n$. First, for $0<α<1$, we establish quantitative transversal and modulus criteria for the global $α$-Hölder continuity of $u$. Then, we construct lacunary examples to show that these criteria are invalid when $α=1$. Finally, under additional integral conditions, we obtain the corresponding global Lipschitz continuity and give Dini--Zygmund conditions on the boundary trace that ensure the Lipschitz continuity.
Source: arXiv (Cornell University)
Authors: Tan, Suling, Li, Hong-Ping
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G260096214
OpenAlex ID: W7203650996