Powered by OpenAIRE graph
Found an issue? Give us feedback
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ ZENODOarrow_drop_down
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Other literature type . 2025
License: CC BY
Data sources: ZENODO
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
ZENODO
Other literature type . 2025
License: CC BY
Data sources: ZENODO
https://doi.org/10.2139/ssrn.5...
Article . 2025 . Peer-reviewed
Data sources: Crossref
ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2026
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2025
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2025
License: CC BY
Data sources: Datacite
versions View all 5 versions
addClaim

Ricci Flow and the Omega-Frame: A Lens-Relative Reading of Perelman's Approach to the Poincaré Conjecture

Authors: Yuan, Mingjing;

Ricci Flow and the Omega-Frame: A Lens-Relative Reading of Perelman's Approach to the Poincaré Conjecture

Abstract

This short note does not contain any new geometric results. Its aim is purely explanatory: to read the core dynamical mechanisms in Perelman’s Ricci flow approach to the Poincaré conjecture through the quotient-typed Scan-Reconfigure metatheory developed in the main Omega-Frame paper. Using the checklist headings (Chk1–Chk8) from the main Omega-Frame paper only as loose navigation labels for interface roles (not as verified hypotheses and not as an item-by-item checklist instantiation), we schematically view Ricci flow with surgery as a lens-relative Scan–Reconfigure system equipped with a time skeleton, a monotone potential, a numerical headroom gauge, and an envelope that describes the coarse-grained range of admissible geometric futures. We then suggest that this irreversibility echoes the No Global Two-Sided Rollback pattern studied in the main paper. The note is addressed to readers already familiar with standard expositions of Perelman’s work who wish to see how its structure fits into the unified Omega-Frame/Scan–Reconfigure interface.

  • BIP!
    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    0
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Average
Powered by OpenAIRE graph
Found an issue? Give us feedback
selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green