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- W2989761214 abstract "Motivated by an example of Shih, we compute the fundamental gap of a family of convex domains in the hyperbolic plane $mathbb H^2$, showing that for some of them $lambda_2 - lambda_1 < frac{3pi^2}{D^2}$, where $D$ is the diameter of the domain and $lambda_1$, $lambda_2$ are the first and second Dirichlet eigenvalues of the Laplace operator on the domain. The result contrasts with what is known in $mathbb R^n $ or $mathbb S^n$, where $lambda_2 - lambda_1 geq frac{3 pi^2}{D^2}$ for convex domains. We also show that the fundamental gap of the example in Shih's article is still greater than $tfrac 32 frac{pi^2}{D^2}$, even though the first eigenfunction of the Laplace operator is not log-concave." @default.
- W2989761214 created "2019-12-05" @default.
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- W2989761214 date "2021-01-01" @default.
- W2989761214 modified "2023-10-18" @default.
- W2989761214 title "Explicit fundamental gap estimates for some convex domains in $mathbb{H}^2$" @default.
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- W2989761214 doi "https://doi.org/10.4310/mrl.2021.v28.n5.a2" @default.
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