Xuan Yao

activity

20232026

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5 papers · 1 filter

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…

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

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

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