Compact capture and protected bridges on the Koras–Russell cylinder
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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.
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Research details
- Subjects
- Mathematics · Complex Analysis · Geometry
- Keywords
- Complex Analysis, Geometry, mathematical research
- Manuscript date
- 2026-10-24
- Reader reuse
- No additional permission granted
Scope
Qualitative holomorphic compact-capture criteria on an adapted Koras–Russell cylinder, including protected thick bridges under explicit hull, Runge and convexity hypotheses.
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.
Reproduction
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.