A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus

Ilka Agricola , Bernd Ammann , Thomas Friedrich

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classification 🧮 math.DG

keywords diraceigenvalueslaplaceoperatortorustwo-dimensionalcomparecomparison

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We compare the eigenvalues of the Dirac and Laplace operator on a two-dimensional torus with respect to the trivial spin structure. In particular, we compute their variation up to order 4 upon deformation of the flat metric, study the corresponding Hamiltonian and discuss several families of examples.

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A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus

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