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

Yuhang Zhao

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

Differential Geometry 2023-07-20 v3

Authors: Yuhang Zhao

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.

Keywords

laplacian eigenvalues laplacian eigenfunctions

Cite

@article{arxiv.2304.06524,
  title  = {First eigenvalue of embedded minimal surfaces in $S^3$},
  author = {Yuhang Zhao},
  journal= {arXiv preprint arXiv:2304.06524},
  year   = {2023}
}

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