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- W2914257966 abstract "Let $$M^n=[0,R]times mathbb {S}^{n-1}$$ be an n-dimensional ( $$nge 2$$ ) smooth Riemannian manifold equipped with the warped product metric $$g=dr^2+h^2(r)g_{mathbb {S}^{n-1}}$$ and diffeomorphic to a Euclidean ball. Assume that M has strictly convex boundary. First, for the classical Steklov eigenvalue problem, we obtain an optimal lower (upper, respectively) bound for its spectrum in terms of $$h'(R)/h(R)$$ when $$mathrm {Ric}_gge 0$$ ( $$le 0$$ , respectively). Second, for two fourth-order Steklov eigenvalue problems studied by Kuttler and Sigillito in 1968, we derive a lower bound for their spectra in terms of either $$h'(R)/h^3(R)$$ or $$h'(R)/h(R)$$ when $$mathrm {Ric}_gge 0$$ , which is optimal for certain cases; in particular, we confirm a conjecture raised by Q. Wang and C. Xia for warped product manifolds of dimension $$n=2$$ or $$nge 4$$ . For some proofs we utilize the Reilly’s formula and reveal a new feature on its use." @default.
- W2914257966 created "2019-02-21" @default.
- W2914257966 creator A5090068762 @default.
- W2914257966 date "2022-02-26" @default.
- W2914257966 modified "2023-10-04" @default.
- W2914257966 title "On the Spectra of Three Steklov Eigenvalue Problems on Warped Product Manifolds" @default.
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- W2914257966 doi "https://doi.org/10.1007/s12220-022-00889-0" @default.
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