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- W4385890342 abstract "Consider a Dirac operator on an oriented compact surface endowed with a Riemannian metric and spin structure. Provided the area and the conformal class are fixed, how small can the $k$-th positive Dirac eigenvalue be? This problem mirrors the maximization problem for the eigenvalues of the Laplacian, which is related to the study of harmonic maps into spheres. We uncover the connection between the critical metrics for Dirac eigenvalues and harmonic maps into complex projective spaces. Using this approach we show that for many conformal classes on a torus the first nonzero Dirac eigenvalue is minimised by the flat metric. We also present a new geometric proof of Bar's theorem stating that the first nonzero Dirac eigenvalue on the sphere is minimised by the standard round metric." @default.
- W4385890342 created "2023-08-17" @default.
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- W4385890342 date "2023-08-15" @default.
- W4385890342 modified "2023-09-27" @default.
- W4385890342 title "Dirac Eigenvalue Optimisation and Harmonic Maps to Complex Projective Spaces" @default.
- W4385890342 doi "https://doi.org/10.48550/arxiv.2308.07875" @default.
- W4385890342 hasPublicationYear "2023" @default.
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