arXiv Open Access 2024

Upper bound for Steklov eigenvalues of warped products with fiber of dimension 2

Jade Brisson Bruno Colbois

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Abstrak

In this note, we investigate the Steklov spectrum of the warped product $[0,L]\times_h Σ$ equipped with the metric $dt^2+h(t)^2g_Σ$, where $Σ$ is a compact surface. We find sharp upper bounds for the Steklov eigenvalues in terms of the eigenvalues of the Laplacian on $Σ$. 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.

Topik & Kata Kunci

math.SP math.DG

Penulis (2)

Jade Brisson

Bruno Colbois

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APA MLA BibTeX

Brisson, J., Colbois, B. (2024). Upper bound for Steklov eigenvalues of warped products with fiber of dimension 2. https://arxiv.org/abs/2403.13620

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓