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- W2905232227 abstract "The main result of this paper is a sharp upper bound on the first positive eigenvalue of Dirac operators in two dimensional simply connected $C^3$-domains with infinite mass boundary conditions. This bound is given in terms of a conformal variation, explicit geometric quantities and of the first eigenvalue for the disk. Its proof relies on the min-max principle applied to the squares of these Dirac operators. A suitable test function is constructed by means of a conformal map. This general upper bound involves the norm of the derivative of the underlying conformal map in the Hardy space $mathcal{H}^2(mathbb{D})$. Then, we apply known estimates of this norm for convex and for nearly circular, star-shaped domains in order to get explicit geometric upper bounds on the eigenvalue. These bounds can be re-interpreted as reverse Faber-Krahn-type inequalities under adequate geometric constraints." @default.
- W2905232227 created "2018-12-22" @default.
- W2905232227 creator A5064042185 @default.
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- W2905232227 date "2019-04-08" @default.
- W2905232227 modified "2023-10-16" @default.
- W2905232227 title "A Sharp Upper Bound on the Spectral Gap for Graphene Quantum Dots" @default.
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- W2905232227 doi "https://doi.org/10.1007/s11040-019-9310-z" @default.
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