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arXiv · 2304.06524

First eigenvalue of embedded minimal surfaces in $S^3$

Yuhang Zhao
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Abstract

We prove that for an embedded minimal surface $\Sigma$ in $S^3$, the first eigenvalue of the Laplacian operator $\lambda_1$ satisfies $\lambda_1\geq 1+\epsilon_g$, where $\epsilon_g>0$ is a constant depending only on the genus $g$ of $\Sigma$. This improves previous result of Choi-Wang.

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Yuhang Zhao. 2023-04-13. First eigenvalue of embedded minimal surfaces in $S^3$. https://arxiv.org/abs/2304.06524

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