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
- 1 · Permanent link
Overview
Abstract
On an adapted model of the Koras-Russell cylinder, we give explicit compression of a closed C-star carrier and a sufficient criterion for ambient compact capture: the planar polynomial hull of the scalar image under q = xy+1 must avoid 1. This yields fixed Runge capture domains, including the connected inverse image of the plane slit along [1,infinity). Joint capture can be corrected to approximate the identity on a globally holomorphically convex parametrized ball inside a fixed Runge Euclidean domain. Prescribed compact bridges of positive thickness can thus be captured while protecting the ball without scalar-range separation. A complementary convex-ball argument treats certain protected bodies through q=1, and an analytic disk explains the obstruction to extending weighted contraction to the entire punctured chart. These are qualitative capture criteria, not a biholomorphic identification of the whole cylinder with C^4 or an improved stabilization bound.
Keywords Complex Analysis · Geometry · mathematical research
Scope of the work
Explicit KR-cylinder carrier; sufficient scalar-hull/fixed-cut capture; protected prescribed bridges within these domains; separate joint-convex q=1 ball protection. No global stabilization or arbitrary bridge theorem.
Reproduction notes
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The manuscript
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Author disclosures
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A stable scholarly record
Cite this edition
Scott Schubr. (2026). Compact capture and protected bridges on the Koras–Russell cylinder (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/compact-capture-and-protected-bridges-on-the-koras-russell-cylinder/v/1
BibTeX
@techreport{luminary_compact_capture_and_protected_bridges_on_the_koras_russell_cylinder_v1,
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 1},
url = {https://research.luminaryoddities.com/compact-capture-and-protected-bridges-on-the-koras-russell-cylinder/v/1}
}Loading discussion…