From the 1 of 6 linked papers with an AI index.
4 papers · 1 filter
Drawstrings and flexibility in the Geroch conjecture
Demetre Kazaras, Kai Xu
The paper constructs warped‑product 3‑manifolds with almost nonnegative scalar curvature that converge to pulled‑string spaces, providing a counterexample to a stability conjecture…
Scalar curvature and volume entropy of hyperbolic 3-manifolds
Demetre Kazaras, Antoine Song, Kai Xu
We show that any closed hyperbolic 3-manifold M admits a Riemannian metric with scalar curvature at least -6, but with volume entropy strictly larger than 2. In particular, this co…
3-Manifolds with positive scalar curvature and bounded geometry
Otis Chodosh, Yi Lai, Kai Xu
We show that a complete contractible 3-manifold with positive scalar curvature and bounded geometry must be . We also show that an open handlebody of genus larger than…
Codimension 2 drawstrings with scalar curvature lower bounds
Demetre Kazaras, Kai Xu
We produce new examples of Riemannian manifolds with scalar curvature lower bounds and collapsing behavior along codimension 2 submanifolds. Applications of this construction are g…