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arXiv · 2511.08228

Pairs of Embedded Spheres with Pinched Prescribed Mean Curvature

Liam Mazurowski·Xin Zhou
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Abstract

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-spheres with prescribed mean curvature $h$. The same result holds for sign-changing functions $h$ satisfying $\vert h\vert < h_0$ under a mild assumption on the zero set.

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Liam Mazurowski, Xin Zhou. 2025-11-11. Pairs of Embedded Spheres with Pinched Prescribed Mean Curvature. https://arxiv.org/abs/2511.08228

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