We develop a suitable generalization of Almgren's theory of varifolds in a Lorentzian setting, focusing on area, first variation, rectifiability, compactness, and closure issues. Motivated by the asymptotic behaviour of the scaled hyperbolic Ginzburg-Landau equations, and by the presence of singularities in Lorentzian minimal surfaces, we introduce, within the varifold class, various notions of generalized minimal time-like submanifolds of arbitrary codimension in flatMinkowski spacetime, which are global in character and admit conserved quantities, such as relativistic energy and momentum. In particular, we show that stationary Lorentzian 2-varifolds properly include the class of classical relativistic and subrelativistic strings. We also discuss several examples.
Lorentzian varifolds and applications to relativistic strings
NOVAGA, MATTEO;
2012-01-01
Abstract
We develop a suitable generalization of Almgren's theory of varifolds in a Lorentzian setting, focusing on area, first variation, rectifiability, compactness, and closure issues. Motivated by the asymptotic behaviour of the scaled hyperbolic Ginzburg-Landau equations, and by the presence of singularities in Lorentzian minimal surfaces, we introduce, within the varifold class, various notions of generalized minimal time-like submanifolds of arbitrary codimension in flatMinkowski spacetime, which are global in character and admit conserved quantities, such as relativistic energy and momentum. In particular, we show that stationary Lorentzian 2-varifolds properly include the class of classical relativistic and subrelativistic strings. We also discuss several examples.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
