Nonlinear Dirac Equations, Monotonicity Formulas and Liouville Theorems-Reference-Cited by-同舟云学术

Nonlinear Dirac Equations, Monotonicity Formulas and Liouville Theorems

Published:2019-11-13 Issue:3 Volume:372 Page:733-767
ISSN:0010-3616
Container-title:Communications in Mathematical Physics
language:en
Short-container-title:Commun. Math. Phys.

Author:

Branding Volker^ORCID

Abstract

Abstract We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we derive monotonicity formulas and Liouville theorems for solutions of these equations. Finally, we extend our analysis to Dirac-harmonic maps with curvature term.

Funder

Austrian Science Fund

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

http://link.springer.com/content/pdf/10.1007/s00220-019-03608-z.pdf

Reference39 articles.

1. Ammann, B.: The smallest Dirac eigenvalue in a spin-conformal class and cmc immersions. Commun. Anal. Geom. 17(3), 429–479 (2009)

2. Bär, C.: Real Killing spinors and holonomy. Commun. Math. Phys. 154(3), 509–521 (1993)

3. Bär, C.: Zero sets of solutions to semilinear elliptic systems of first order. Invent. Math. 138(1), 183–202 (1999)

4. Bär, C., Gauduchon, P., Moroianu, A.: Generalized cylinders in semi-Riemannian and spin geometry. Math. Z. 249(3), 545–580 (2005)

5. Bartnik, R.A., Chruściel, P.T.: Boundary value problems for Dirac-type equations. J. Reine Angew. Math. 579, 13–73 (2005)

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Dirac-harmonic maps with potential;Letters in Mathematical Physics;2022-07-02

2. A spinorial analogue of the Brezis-Nirenberg theorem involving the critical Sobolev exponent;Journal of Functional Analysis;2021-06

3. On the Evolution of Regularized Dirac-Harmonic Maps from Closed Surfaces;Results in Mathematics;2020-03-18