AIM-SEVERAL_COMPLEX_VARIABLES-0021 · Complete counterexample

A Nonremovable Meromorphic Map into a Ball on a Codimension-Two Wedge

Manuscript 10 October 2026 · Online 10 October 2026

math.CVUnrefereed preprint

Abstract

We construct a meromorphic germ in C^3 that is holomorphic from an attached wedge into the open unit ball, extends continuously to its real-algebraic generic edge with values on the unit sphere, and nevertheless has no holomorphic extension to a full neighborhood of the edge point. The edge has real codimension two and CR dimension one. An explicit rational sphere identity is combined with a holomorphic factor that is unimodular on the edge and suppresses interior norm growth. The boundary limit holds along every wedge approach, not just normal rays. This gives a negative answer to the arbitrary-generic-edge question posed by Meylan in the 2010 AIM CR-mapping problem list, with convergence understood from inside the ball. The example is nonminimal and has a continuous but nondifferentiable boundary map; it makes no claim about strengthened minimal-source or smooth-boundary-map formulations. The manuscript is AI-assisted, self-audited and unrefereed. No independent review, formal verification or absolute priority is claimed.

Record

Affiliation
Mercury Software GmbH
Result
Complete counterexample
Categories
math.CV
Manuscript
10 October 2026
Online release
10 October 2026
Version
1.0
License
Creative Commons Attribution 4.0 International

Files and verification

The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.

Citation

Alper Ferudun, “A Nonremovable Meromorphic Map into a Ball on a Codimension-Two Wedge,” EulerSolve Research Papers, AIM-SEVERAL_COMPLEX_VARIABLES-0021, 2026. https://doi.org/10.5281/zenodo.23272827.

BibTeX
@misc{Ferudun2026MeromorphicWedge,
  author = {Ferudun, Alper},
  title = {A Nonremovable Meromorphic Map into a Ball on a Codimension-Two Wedge},
  year = {2026},
  howpublished = {EulerSolve Research Papers},
  url = {https://eulersolve.org/papers/aim-several-complex-variables-0021/},
  doi = {10.5281/zenodo.23272827},
  note = {AIM-SEVERAL_COMPLEX_VARIABLES-0021; unrefereed preprint}
}

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