Abstract
We observe that the maximal open set of constant curvature κ in a Riemannian manifold of curvature ≥ κ or 6 ≤ κ has a convexity-type property, which we call two-convexity. This statement is used to prove a number of rigidity statements in comparison geometry.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 617-631 |
| Number of pages | 15 |
| Journal | Geometry and Topology |
| Volume | 18 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 30 2014 |
All Science Journal Classification (ASJC) codes
- Geometry and Topology
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Cite this
Panov, D., & Petrunin, A. (2014). Sweeping out sectional curvature. Geometry and Topology, 18(2), 617-631. https://doi.org/10.2140/gt.2014.18.617