PreprintarXiv licencearXiv
Transversal Hölder Criteria and Dini--Zygmund Endpoint Regularity for Hyperbolic Harmonic Mappings
Abstract
Let n≥3, and let u be a bounded hyperbolic harmonic mapping on the real hyperbolic upper half-space ℍn. 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.
Related
- September 2026 Working Notes on 3D Navier–Stokes Conditional Regularity Criteria, the Hodge–Navier–Stokes Architecture Referee Audit, and Triadic Multiscale Homogenization
- Maximal Regularity and Existence for Superquadratic Parabolic Hamilton--Jacobi Equations: The Endpoint case
- Endpoint Maximal Regularity for Superquadratic Hamilton-Jacobi Equations and Applications to Ergodic Mean-field Games Systems
- Endpoint estimates for spherical maximal operators acting on radial functions in hyperbolic spaces
- Regularity of profinite isomorphisms of hyperbolic 3-manifolds
BibTeX
@misc{tan2026transversal,
title = {{Transversal Hölder Criteria and Dini--Zygmund Endpoint Regularity for Hyperbolic Harmonic Mappings}},
author = {Suling Tan and Hong-Ping Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.13927},
eprint = {2608.13927},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.13927},
}
RIS
TY - UNPB
TI - Transversal Hölder Criteria and Dini--Zygmund Endpoint Regularity for Hyperbolic Harmonic Mappings
AU - Suling Tan
AU - Hong-Ping Li
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2608.13927
UR - https://arxiv.org/abs/2608.13927
AB - Let n≥3, and let u be a bounded hyperbolic harmonic mapping on the real hyperbolic upper half-space 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.
ER -