Xuan Yao

activity

20242026

collaborators

10 papers

math.DG2026

Rigidity in the Positive Mass Theorem with $C^{0}$ Decay

Liam Mazurowski, Xuan Yao

Let $g$ be a smooth metric on $R^{3}$ with non-negative scalar curvature. We show that if $g$ satisfies $∣ g (x) - g_{euc} (x) ∣ = O (∣ x ∣^{- 1 - I ¨ })$ for some…

math.DG2026

A Positive Mass Theorem for Continuous Metrics

Liam Mazurowski, Xuan Yao

Let $g$ be a continuous metric on $R^{3}$ which is asymptotically flat in the sense that $∣ g_{ij} (x) - I^´_{ij} ∣ = O (∣ x ∣^{- I ¨ })$ for some $I ¨ > \frac{1}{2}$ .…

math.DG2026

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 $M_{k}$ and $M$ are…

math.DG2026

Quantification of $C^{0}$ Convergence in Dimension Three

Liam Mazurowski, Xuan Yao

We address Gromov's Quantification of $C^{0}$ Convergence Conjecture in dimension three. Let $B$ be the unit ball in $R^{3}$ . Let $g$ and $g_{0}$ be smooth metrics on $B$ . We pro…

math.DG2026

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…

math.DG2025

Scalar curvature comparison and rigidity of $3$ -dimensional weakly convex domains

Dongyeong Ko, Xuan Yao

For a compact Riemannian $3$ -manifold $(M^{3}, g)$ with mean convex boundary which is diffeomorphic to a weakly convex compact domain in $R^{3}$ , we prove that if scalar c…

Rigidity in the Positive Mass Theorem with C0 Decay

A Positive Mass Theorem for Continuous Metrics

Scalar curvature under weak limits of manifolds

Quantification of C0 Convergence in Dimension Three

Capillary minimal slicing and scalar curvature rigidity

Scalar curvature comparison and rigidity of 3-dimensional weakly convex domains

Rigidity in the Positive Mass Theorem with $C^{0}$ Decay

Quantification of $C^{0}$ Convergence in Dimension Three

Scalar curvature comparison and rigidity of $3$ -dimensional weakly convex domains