Spinor pairs and the concentration principle for Dirac operators
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- by Manousos Maridakis PDF
- Trans. Amer. Math. Soc. 369 (2017), 2231-2254 Request permission
Abstract:
We study perturbed Dirac operators of the form $D_s= D + s\mathcal {A} :\Gamma (E)\rightarrow \Gamma (F)$ over a compact Riemannian manifold $(X, g)$ with symbol $c$ and special bundle maps $\mathcal {A} : E\rightarrow F$ for $s \gg 0$. Under a simple algebraic criterion on the pair $(c, \mathcal {A})$, solutions of $D_s\psi =0$ concentrate as $s\to \infty$ around the singular set $Z_{\mathcal {A}}\subset X$ of $\mathcal {A}$. We give many examples, the most interesting ones arising from a general โspinor pairโ construction.References
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Additional Information
- Manousos Maridakis
- Affiliation: Department of Mathematics, Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
- Email: mmanos@math.rutgers.edu
- Received by editor(s): June 19, 2015
- Received by editor(s) in revised form: June 27, 2015, and October 16, 2015
- Published electronically: October 7, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 2231-2254
- MSC (2010): Primary 53C27; Secondary 58J37
- DOI: https://doi.org/10.1090/tran/6858
- MathSciNet review: 3581233