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The Dolbeault operator on Hermitian spin surfaces

Bodgan Alexandrov, Gueo Grantcharov, Stefan Ivanov (2001)

Annales de l’institut Fourier

We prove the vanishing of the kernel of the Dolbeault operator of the square root of the canonical line bundle of a compact Hermitian spin surface with positive scalar curvature. We give lower estimates of the eigenvalues of this operator when the conformal scalar curvature is non -negative.

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