Xin Zhou

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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.DG2024

An Alternative for Constant Mean Curvature Hypersurfaces

Liam Mazurowski, Xin Zhou

Let $M^{n + 1}$ be a closed manifold of dimension $3 \leq n + 1 \leq 7$ equipped with a generic Riemannian metric $g$ . Let $c$ be a positive number. We show that, either there exist infini…

math.DG2024

Infinitely Many Half-Volume Constant Mean Curvature Hypersurfaces via Min-Max Theory

Liam Mazurowski, Xin Zhou

Let $(M^{n + 1}, g)$ be a closed Riemannian manifold of dimension $3 \leq n + 1 \leq 5$ . We show that, if the metric $g$ is generic or if the metric $g$ has positive Ricci curvature, then $…