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Research Article | Open Access

Value of first eigenvalue of some minimal hypersurfaces embedded in the unit sphere

Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P. O. Box-65892, Riyadh 11566, Saudi Arabia
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Abstract

We prove that the first nonzero eigenvalue of the Laplace-Beltrami operator of equator-like minimal submanifold embedded in the sphere S n + 1 is equal to n. The proof uses the spectral properties of the heat kernel operator corresponding to the submanifold.

Keywords

minimal submanifoldsLaplace operatoreigenvaluesheat kernel
CLC number: 47A75, 53A10, 53C42

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 26532-26542
DOI: 10.3934/math.20231355

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Cite this article:
Aldayel I. Value of first eigenvalue of some minimal hypersurfaces embedded in the unit sphere. AIMS Mathematics, 2023, 8(11): 26532-26542. https://doi.org/10.3934/math.20231355

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Received: 18 July 2023
Revised: 22 August 2023
Accepted: 27 August 2023
Published: 15 November 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)