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Upper bound for Steklov eigenvalues of warped products with fiber of dimension 2 (2403.13620v2)
Published 20 Mar 2024 in math.SP and math.DG
Abstract: In this note, we investigate the Steklov spectrum of the warped product $[0,L]\times_h \Sigma$ equipped with the metric $dt2+h(t)2g_\Sigma$, where $\Sigma$ is a compact surface. We find sharp upper bounds for the Steklov eigenvalues in terms of the eigenvalues of the Laplacian on $\Sigma$. We apply our method to the case of metric of revolution on the 3-dimensional ball and we obtain a sharp estimate on the spectral gap between two consecutive Steklov eigenvalues.
- Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator. Bull. Math. Sci., 2(1):1–56, 2012.
- Spectral ratios for Steklov eigenvalues of balls with revolution-type metrics, 2024.
- Compact manifolds with fixed boundary and large Steklov eigenvalues. Proc. Amer. Math. Soc., 147(9):3813–3827, 2019.
- Some recent developments on the Steklov eigenvalue problem, 2023. arXiv:2212.12528, to appear at Revista Matemática Complutense; published online.
- Richard S. Laugesen. The Robin Laplacian—Spectral conjectures, rectangular theorems. J. Math. Phys., 60(12):121507, 31, 2019.
- Changwei Xiong. Optimal estimates for Steklov eigenvalue gaps and ratios on warped product manifolds. Int. Math. Res. Not. IMRN, (22):16938–16962, 2021.
- Changwei Xiong. On the spectra of three Steklov eigenvalue problems on warped product manifolds. J. Geom. Anal., 32(5):Paper No. 153, 35, 2022.
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