The First Eigenvalue of Dirac and Laplace Operators on Surfaces
نویسنده
چکیده
Let (M, g, σ) be a compact Riemannian surface equipped with a spin structure σ. For any metric ḡ onM , we denote by ΣḡM the spinor bundle associated to ḡ. We let ∆ḡ be the Laplace-Beltrami operator acting on smooth functions of M and Dḡ be the Dirac operator acting on smooth spinor fields with respect to the metric ḡ. We also denote by μ1(ḡ) (resp. λ1(ḡ)) the smallest positive eigenvalue of ∆ḡ (resp. Dḡ). Agricola, Ammann and Friedrich asked the following question in [AAF99]:
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