PreprintarXiv licencearXiv
Einstein four-manifolds of positive sectional curvature and ADM mass
Abstract
We prove that closed Einstein four-manifolds (M,g) with positive sectional curvature and Euler characteristic and signature satisfying 2χ(M)−3|τ(M)|≤4 must be homothetically isometric to the round S4 or to ℂℙ2 with the Fubini-Study metric. The proof relies on an upper bound on the ADM mass of conformal blow-ups of (M,g), combined with a lower one from \cite{GM}.
Related
- Convergence of cohomogeneity-one Lagrangian mean curvature flow in positive Kähler-Einstein manifolds
- Positive Einstein metrics on infinitely many four-manifolds
- Collapse to nonsmoothable manifolds under lower sectional and positive Ricci curvature bounds
- Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature
- Hessian manifolds of positive constant Hessian sectional curvature
BibTeX
@misc{gursky2026einstein,
title = {{Einstein four-manifolds of positive sectional curvature and ADM mass}},
author = {Matthew Gursky and Andrea Malchiodi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30803},
eprint = {2609.30803},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30803},
}
RIS
TY - UNPB
TI - Einstein four-manifolds of positive sectional curvature and ADM mass
AU - Matthew Gursky
AU - Andrea Malchiodi
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30803
UR - https://arxiv.org/abs/2609.30803
AB - We prove that closed Einstein four-manifolds (M,g) with positive sectional curvature and Euler characteristic and signature satisfying 2χ(M)−3|τ(M)|≤4 must be homothetically isometric to the round S^4 or to ℂℙ^2 with the Fubini-Study metric. The proof relies on an upper bound on the ADM mass of conformal blow-ups of (M,g), combined with a lower one from \cite{GM}.
ER -