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arXiv · 1607.08306

Partial result of Yau's Conjecture of the first eigenvalue in unit sphere $\mathbb{S}^{n+1}(1)$

Zhongyang Sun
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Abstract

In this paper, we partially solve Yau' Conjecture of the first eigenvalue of an embedded compact minimal hypersurface of unit sphere $\mathbb{S}^{n+1}(1)$, i.e., Corollary 1.2. In particular, Corollary 1.3 proves that the condition $\int_{\Omega_{1}}|\nabla u|^{2}=(n+1)\int_{\Omega_{1}}u^{2}$ is naturally true and meaningful in Corollary 1.2.

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Zhongyang Sun. 2016-07-28. Partial result of Yau's Conjecture of the first eigenvalue in unit sphere $\mathbb{S}^{n+1}(1)$. https://arxiv.org/abs/1607.08306

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