English

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

Differential Geometry 2016-08-02 v2

Abstract

In this paper, we partially solve Yau' Conjecture of the first eigenvalue of an embedded compact minimal hypersurface of unit sphere Sn+1(1)\mathbb{S}^{n+1}(1), i.e., Corollary 1.2. In particular, Corollary 1.3 proves that the condition Ω1u2=(n+1)Ω1u2\int_{\Omega_{1}}|\nabla u|^{2}=(n+1)\int_{\Omega_{1}}u^{2} is naturally true and meaningful in Corollary 1.2.

Keywords

Cite

@article{arxiv.1607.08306,
  title  = {Partial result of Yau's Conjecture of the first eigenvalue in unit sphere $\mathbb{S}^{n+1}(1)$},
  author = {Zhongyang Sun},
  journal= {arXiv preprint arXiv:1607.08306},
  year   = {2016}
}