Cipriana Anghel-Stan, Universität Göttingen
On the spectrum of the Dirac operator on degenerating Riemannian surfaces
Nov 4, 2024, 14:15
We study the behavior of the spectrum of the Dirac operator on
degenerating families of compact Riemannian surfaces,
when the length of a simple closed geodesic shrinks to zero,
under the hypothesis that the spin structure along the pinched geodesic
is non-trivial.
The difficulty of the problem stems from the non-compactness of the limit surface, which has finite area and two cusps. The main idea in this investigation is to construct an adapted pseudodifferential calculus, in the spirit of the celebrated \emph{b}-algebra of Melrose, which includes both the family of Dirac operators on the family of compact surfaces and the
Dirac operator on the limit non-compact surface,
together with their resolvents.
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