8 papers
Scalar curvature under weak limits of manifolds
Liam Mazurowski, Xuan Yao
We show that scalar curvature lower bounds are preserved under certain weak convergence of smooth three manifolds to a smooth limit. More precisely, suppose that and are…
Quantification of Convergence in Dimension Three
Liam Mazurowski, Xuan Yao
We address Gromov's Quantification of Convergence Conjecture in dimension three. Let be the unit ball in . Let and be smooth metrics on . We pro…
Capillary minimal slicing and scalar curvature rigidity
Dongyeong Ko, Xuan Yao
We develop minimal slicing via capillary hypersurfaces to understand positive scalar curvature metric on manifolds with boundary. The method provides rigidity statements once the r…
On the topology of manifolds with positive intermediate curvature
Liam Mazurowski, Tongrui Wang, Xuan Yao
We formulate a conjecture relating the topology of a manifold's universal cover with the existence of metrics with positive -intermediate curvature. We prove the result for mani…
Euclidean Domains with Nearly Maximal Yamabe Quotient
Liam Mazurowski, Xuan Yao
Let be a smooth, bounded domain in with connected boundary. It follows from work of Escobar that the Yamabe quotient of is at most the Yamabe quotient of a ba…
A Note on Scalar curvature comparison rigidity for compact domains
Xuan Yao
We prove a generalization of Gromov's conjecture on scalar curvature rigidity of convex polytopes to arbitrary convex Riemannian polytope type domains via harmonic spinors on conve…