Math RefereeEffective version of Ratner's equidistribution theorem for SL(3,R)
Lei Yang
The proposed argument
The proposed proof translates long unipotent orbit segments into expanding translates, imposes a two-sided diagonal thickness alternative, constructs transverse sets after a nondivergence step, and iterates dimension growth before a high-dimensional equidistribution input. Separate corollaries concern straight lines and nondegenerate planar curves.
Native panel: 63-page arXiv v6. The official Annals article has 76 pages (189–264) and is separately available below; critical passages were directly compared. External-input cutoff: received 26 September 2022.
Reading order
- 01
Statements and the exceptional alternative
Read the vector-and-bivector thick part and the two equivalent formulations, keeping every quantifier and the diagonal exponents.
- 02
Nondivergence and initial transverse sets
Follow the quantitative nondivergence input, the parameter list and the retained-set construction before dimension growth.
- 03
Dimension growth and equidistribution
Trace the multiscale transverse-set estimates into the high-dimensional equidistribution input and the main theorem.
- 04
Applications to curves
Read each expanding-curve corollary separately, including changes of scale and Diophantine conditions.
Follow the dependencies
Open the full map ↗Select a claim to see its prerequisites and consumers. Edge labels distinguish proof inputs, source references, background and exclusions.
Your independent assessment
Trace both formulations, vector/bivector tests, retained-set construction and dimension-growth branches; assess the curve applications separately.