The Dirac operator under collapse to a smooth limit space

Dirac Operators on Hypersurfaces as Large Mass Limits

“…The result of Theorem 3 providing an interpretation of D / using an infinite mass jump on Σ does not seem to have previous analogs. In a sense, it can be viewed as a potential-induced collapse by analogy with Dirac operators on manifolds converging to a lower-dimensional structure [14,16]. As a possible application of our results, we remark that estimating the central gap (i.e.…”

Compactness of Dirac-Einstein spin manifolds and horizontal deformations

“…In fact, if (g, ψ) ∈ Crit c (E), then the lower bound on the Q-curvature is equivalent to our condition −∆ g R g ≥ −KR g . We want to point out that the study of compactness and convergence of manifolds with underlying spinors was investigated in [19,23], also some cases of collapsing along the limit were studied in [30,31]. In our case, the functional provides more control on the spinorial component and this allow us to keep track of its limit.…”