On the second Robin eigenvalue of the Laplacian
Li, Xiaolong Wang, Kui Wu, Haotian
Li, Xiaolong
Wang, Kui
Wu, Haotian
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2023-10
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Li, X., Wang, K. & Wu, H. On the second Robin eigenvalue of the Laplacian. Calc. Var. 62, 256 (2023). https://doi.org/10.1007/s00526-023-02607-2
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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Springer Science and Business Media Deutschland GmbH
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Calculus of Variations and Partial Differential Equations
v.62 no. 9, art. no. 256
v.62 no. 9, art. no. 256
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0944-2669