Partial result of Yau's Conjecture of the first eigenvalue in unit sphere \mathbbSⁿ⁺¹(1)

2016/07/28 by Sun, Zhongyang
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.08306

Abstract

In this paper, we partially solve Yau' Conjecture of the first eigenvalue of an embedded compact minimal hypersurface of unit sphere \mathbbSⁿ⁺¹(1), i.e., Corollary 1.2. In particular, Corollary 1.3 proves that the condition ∫_Ω₁|∇ u|²=(n+1)∫_Ω₁u² is naturally true and meaningful in Corollary 1.2.

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