On the second Robin eigenvalue of the Laplacian

Xiaolong Li; Kui Wang; Haotian Wu

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arXiv · 2003.03087

On the second Robin eigenvalue of the Laplacian

Xiaolong Li·Kui Wang·Haotian Wu

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Abstract

We study the Robin eigenvalue problem for the Laplace-Beltrami operator on Riemannian manifolds. Our first result is a comparison theorem for the second Robin eigenvalue on geodesic balls in manifolds whose sectional curvatures are bounded from above. Our second result asserts that geodesic balls in nonpositively curved space forms maximize the second Robin eigenvalue among bounded domains of the same volume.

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BibTeX RIS

Xiaolong Li, Kui Wang, Haotian Wu. 2020-03-06. On the second Robin eigenvalue of the Laplacian. https://arxiv.org/abs/2003.03087

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