FIRST EIGENVALUE CHARACTERISATION OF CLIFFORD HYPERSURFACES AND VERONESE SURFACES

Pub Date : 2024-04-25 DOI:10.1017/s0004972724000273
PEIYI WU
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Abstract

We give a sharp estimate for the first eigenvalue of the Schrödinger operator $L:=-\Delta -\sigma $ which is defined on the closed minimal submanifold $M^{n}$ in the unit sphere $\mathbb {S}^{n+m}$ , where $\sigma $ is the square norm of the second fundamental form.
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clifford 超曲面和 veronese 曲面的第一特征值表征
我们给出了薛定谔算子$L:=-\Delta -\sigma $的第一个特征值的尖锐估计值,该算子定义在单位球$\mathbb {S}^{n+m}$ 中的封闭最小子球面$M^{n}$上,其中$\sigma $是第二基本形式的平方规范。
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