Liam Mazurowski

activity

20242026

collaborators

9 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.DG2025

Pairs of Embedded Spheres with Pinched Prescribed Mean Curvature

Liam Mazurowski, Xin Zhou

Assume $h$ is a positive function on the unit three-sphere which satisfies the pinching condition $h < h_{0} \approx 0.547$ . We prove the existence of at least two embedded two-spher…

math.DG2025

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 $m$ -intermediate curvature. We prove the result for mani…

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

Pairs of Embedded Spheres with Pinched Prescribed Mean Curvature

On the topology of manifolds with positive intermediate curvature

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

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