Research Article · Preprint Mathematics
Compact capture and protected bridges on the Koras–Russell cylinder
- Primary subject
- Mathematics
- Subject subfields
- Complex Analysis · Geometry
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 2 · Permanent link
Overview
Abstract
On an adapted model of the Koras–Russell cylinder, we give an explicit compression of a closed ℂ^* carrier and a sufficient condition for ambient compact capture: the planar polynomial hull of the scalar image under q=xy+1 must avoid 1. The construction yields fixed Runge capture domains, including the connected domain q^(-1)(ℂ∖[1,∞)). Joint capture can be corrected to approximate the identity on a globally holomorphically convex parametrized ball in a fixed Runge Euclidean domain. This gives protected capture of prescribed compact bridges of positive thickness, with no separation of the moving and protected scalar ranges. A complementary convex-ball argument treats certain protected bodies through q=1. An analytic disk explains why the weighted contraction cannot simply be extended to the entire punctured chart. The results are qualitative capture criteria.
Keywords Complex Analysis · Geometry · mathematical research
Scope of the work
Qualitative holomorphic compact-capture criteria on an adapted Koras–Russell cylinder, including protected thick bridges under explicit hull, Runge and convexity hypotheses.
Reproduction notes
8-page manuscript and 6 source-package members. Compile main.tex with a compatible LaTeX engine. The capture criteria and protected-bridge results are analytic and require no numerical supplement.
The manuscript
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Author disclosures
AI-assisted tools supported research exploration, literature review, manuscript preparation and internal verification. The author retains responsibility for the work. Internal AI-assisted and computational checks are distinct from external human peer review.
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Cite this edition
Scott Schubr. (2026). Compact capture and protected bridges on the Koras–Russell cylinder (Version 2). Luminary Research Archive. https://research.luminaryoddities.com/compact-capture-and-protected-bridges-on-the-koras-russell-cylinder/v/2
BibTeX
@techreport{luminary_compact_capture_and_protected_bridges_on_the_koras_russell_cylinder_v2,
title = {Compact capture and protected bridges on the Koras–Russell cylinder},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 2},
url = {https://research.luminaryoddities.com/compact-capture-and-protected-bridges-on-the-koras-russell-cylinder/v/2}
}Loading discussion…