Generalized Bernstein property and gravitational strings in Born-Infeld theory

Lesley Sibner, Robert Sibner, Yisong Yang

Research output: Contribution to journalArticle

Abstract

Motivated by Born-Infeld geometric electromagnetic theory, we consider a series of nonlinear equations which extend the minimal surface equations and the related, generalized, Bernstein problems. We study the relation of these equations and the conditions which lead to the triviality of the solutions. We also study a non-Abelian extension of these equations and establish a gap theorem for the Yang-Mills-Born-Infeld fields. We then couple the Born-Infeld electromagnetism with a Higgs scalar field and obtain an existence theorem for the self-dual multiple cosmic string solutions on a closed surface characterized jointly by the first Chern class and the Thom class formulated over the hosting complex line bundle.

Original languageEnglish (US)
Article number008
Pages (from-to)1193-1213
Number of pages21
JournalNonlinearity
Volume20
Issue number5
DOIs
StatePublished - May 1 2007

Fingerprint

Born-Infeld theory
strings
Strings
Electromagnetism
Nonlinear equations
existence theorems
electromagnetism
minimal surfaces
Cosmic Strings
Chern Classes
Yang-Mills
Minimal surface
Line Bundle
Higgs
Existence Theorem
Scalar Field
nonlinear equations
bundles
Nonlinear Equations
theorems

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Generalized Bernstein property and gravitational strings in Born-Infeld theory. / Sibner, Lesley; Sibner, Robert; Yang, Yisong.

In: Nonlinearity, Vol. 20, No. 5, 008, 01.05.2007, p. 1193-1213.

Research output: Contribution to journalArticle

Sibner, Lesley ; Sibner, Robert ; Yang, Yisong. / Generalized Bernstein property and gravitational strings in Born-Infeld theory. In: Nonlinearity. 2007 ; Vol. 20, No. 5. pp. 1193-1213.
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