Regime Geometry in Context: Admissibility Collapse, Null Limits, and the Boundary of Classical Geometry

This paper positions Regime Geometry in relation to classical geometry, Ricci flow, and free-boundary methods. Rather than proposing a new geometric evolution, it introduces a framework for analyzing the persistence or collapse of admissibility itself. Using established tools from variational convergence, operator theory, and coercivity analysis, the paper distinguishes classical singularities—where geometry persists—from null limits, where admissible geometric structure ceases to exist. The result is a boundary theory that clarifies when geometric modeling remains valid and when it must terminate.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-12-27
DOI
https://doi.org/10.5281/zenodo.18071890
Primary Topic
Geometric Analysis and Curvature Flows
Type
article
Field-Weighted Citation Impact
0.00
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article

Regime Geometry in Context: Admissibility Collapse, Null Limits, and the Boundary of Classical Geometry

L. D. L. Nguyen
Zenodo (CERN European Organization for Nuclear Research)
Geometric Analysis and Curvature Flows
article

Regime Geometry in Context: Admissibility Collapse, Null Limits, and the Boundary of Classical Geometry

L. D. L. Nguyen
article en

Abstract

This paper positions Regime Geometry in relation to classical geometry, Ricci flow, and free-boundary methods. Rather than proposing a new geometric evolution, it introduces a framework for analyzing the persistence or collapse of admissibility itself. Using established tools from variational convergence, operator theory, and coercivity analysis, the paper distinguishes classical singularities—where geometry persists—from null limits, where admissible geometric structure ceases to exist. The result is a boundary theory that clarifies when geometric modeling remains valid and when it must terminate.

Zenodo (CERN European Organization for Nuclear Research)
Network Rail (GB)
Openalex Percentile: Top 23%
Geometric Analysis and Curvature Flows
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