PreprintarXiv licencearXiv
Ricci flow on manifolds with positive isotropic curvature in all dimensions
Abstract
We extend the classification of manifolds with positive isotropic curvature to all dimensions n ≥ 5. This result also completes the classification of uniformly positive isotropic curvature on complete non-compact κ-noncollapsed ancient solutions and gradient shrinking Ricci solitons. The proof involves a construction of pinching cones in all dimensions, refining and extending to all dimensions the results of the first author. We have used MATHEMATICA to find viable parameters for the cone families. The final presentation is self-contained and can be verified manually. No stage of this work involved LLMs.
Related
- Minimal Two-Spheres and Manifolds with Positive Isotropic Curvature
- Free Circle Actions and Positive Ricci Curvature on Manifolds with the Cohomology Ring of S2× S5
- Collapse to nonsmoothable manifolds under lower sectional and positive Ricci curvature bounds
- Pinching cones for positive isotropic curvature in dimensions seven and eight
- Topology of tame contractible n-manifolds, n=6,7, with Positive BiRicci Curvature and Ricci lower bounds
BibTeX
@misc{brendle2026ricci,
title = {{Ricci flow on manifolds with positive isotropic curvature in all dimensions}},
author = {Simon Brendle and Raphael Tsiamis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02325},
eprint = {2610.02325},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02325},
}
RIS
TY - UNPB
TI - Ricci flow on manifolds with positive isotropic curvature in all dimensions
AU - Simon Brendle
AU - Raphael Tsiamis
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02325
UR - https://arxiv.org/abs/2610.02325
AB - We extend the classification of manifolds with positive isotropic curvature to all dimensions n ≥ 5. This result also completes the classification of uniformly positive isotropic curvature on complete non-compact κ-noncollapsed ancient solutions and gradient shrinking Ricci solitons. The proof involves a construction of pinching cones in all dimensions, refining and extending to all dimensions the results of the first author. We have used MATHEMATICA to find viable parameters for the cone families. The final presentation is self-contained and can be verified manually. No stage of this work involved LLMs.
ER -