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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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