PreprintCC BY 4.0arXiv
Minimal Two-Spheres and Manifolds with Positive Isotropic Curvature
Abstract
We improve the Micallef--Moore index estimate for harmonic two-spheres in n-manifolds with positive isotropic curvature to the sharp bound n−3. Combining with recent work, this completes the diffeomorphism classification of closed manifolds with positive isotropic curvature in the remaining dimensions five and six.
Related
- Ricci flow on manifolds with positive isotropic curvature in all dimensions
- Curvature pinching for minimal Tangent-Yang-Mills hypersurfaces in spheres
- A Curvature Gap for Minimal Submanifolds in Spheres
- The Morse Index, Nullity and Jacobi Fields of Constant-Curvature Minimal 2-Spheres in Complex Projective Spaces
- Hitchin's α-invariant and positive sectional curvature on homotopy $9$-spheres
BibTeX
@misc{chow2026minimal,
title = {{Minimal Two-Spheres and Manifolds with Positive Isotropic Curvature}},
author = {Tsz-Kiu Aaron Chow and Yipeng Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06910},
eprint = {2609.06910},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06910},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Minimal Two-Spheres and Manifolds with Positive Isotropic Curvature
AU - Tsz-Kiu Aaron Chow
AU - Yipeng Wang
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.06910
UR - https://arxiv.org/abs/2609.06910
AB - We improve the Micallef--Moore index estimate for harmonic two-spheres in n-manifolds with positive isotropic curvature to the sharp bound n−3. Combining with recent work, this completes the diffeomorphism classification of closed manifolds with positive isotropic curvature in the remaining dimensions five and six.
ER -