Xuan Yao

activity

20232026

collaborators

14 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 $∣ g (x) - g_{euc} (x) ∣ = O (∣ x ∣^{- 1 - τ})$ 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 $∣ g_{ij} (x) - δ_{ij} ∣ = O (∣ x ∣^{- τ})$ for some $τ > \frac{1}{2}$ . Fur…

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 scalar curvature metric on manifolds bounded below with boundary. In particular, in dimension $4$ , we prove fol…

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…

math.DG2025

Euclidean Domains with Nearly Maximal Yamabe Quotient

Liam Mazurowski, Xuan Yao

Let $Ω$ be a smooth, bounded domain in $R^{3}$ with connected boundary. It follows from work of Escobar that the Yamabe quotient of $Ω$ is at most the Yamabe quotient of a ba…

math.DG2024

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…

math.DG2024

Mass, Conformal Capacity, and the Volumetric Penrose Inequality

Liam Mazurowski, Xuan Yao

Let $Ω$ be a smooth, bounded subset of $R^{3}$ diffeomorphic to a ball. Consider $M = R^{3} ∖ Ω$ equipped with an asymptotically flat metric $g = f^4 g_{\text…

math.DG2024

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…

math.DG2024

Minimal surfaces with low genus in lens spaces

Xingzhe Li, Tongrui Wang, Xuan Yao

Given a Riemannian $RP^{3}$ with a bumpy metric or a metric of positive Ricci curvature, we show that there either exist four distinct minimal real projective planes, or exi…

math.DG2024

On the stability of the Yamabe invariant of $S^{3}$

Liam Mazurowski, Xuan Yao

Let $g$ be a complete, asymptotically flat metric on $R^{3}$ with vanishing scalar curvature. Moreover, assume that $(R^{3}, g)$ supports a nearly Euclidean $L^{2}$ Sobo…

math.DG2023

Generalized $S^{1}$ -stability theorem

Tongrui Wang, Xuan Yao

We use the equivariant $μ$ -bubbles technique to prove that for any compact manifold $M^{n}$ with non-empty boundary, $n \in {3, 5, 6}$ , the Yamabe invariant of $M^{n}$ is positive if and…

math.DG2023

Improved Hebey-Vaugon conjecture on equivariant Yamabe invariants in dimension 3

Tongrui Wang, Xuan Yao

Consider a closed connected $3$ -manifold $M$ acted diffeomorphically on by a compact Lie group $G$ with at least one orbit of finite cardinality. We show an upper bound for the $G$ …

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

On the topology of manifolds with positive intermediate curvature

Euclidean Domains with Nearly Maximal Yamabe Quotient

A Note on Scalar curvature comparison rigidity for compact domains

Mass, Conformal Capacity, and the Volumetric Penrose Inequality

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

Minimal surfaces with low genus in lens spaces

On the stability of the Yamabe invariant of S3

Generalized S1-stability theorem

Improved Hebey-Vaugon conjecture on equivariant Yamabe invariants in dimension 3

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

On the stability of the Yamabe invariant of $S^{3}$

Generalized $S^{1}$ -stability theorem