Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Spinor pairs and the concentration principle for Dirac operators


Author: Manousos Maridakis
Journal: Trans. Amer. Math. Soc. 369 (2017), 2231-2254
MSC (2010): Primary 53C27; Secondary 58J37
DOI: https://doi.org/10.1090/tran/6858
Published electronically: October 7, 2016
MathSciNet review: 3581233
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 ``spinor pair'' construction.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 53C27, 58J37

Retrieve articles in all journals with MSC (2010): 53C27, 58J37


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

DOI: https://doi.org/10.1090/tran/6858
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
Article copyright: © Copyright 2016 American Mathematical Society

American Mathematical Society