Leaf superposition property for integer rectifiable currents
Luigi Ambrosio Gianluca Crippa Philippe G. Lefloch
We consider the class of integer rectifiable currents without boundary in $\R^n\times\R$ satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.
keywords: Metric spaces valued $BV$ functions Multi-valued functions. Integer rectifiable currents Currents in metric spaces Cartesian currents
Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity
Philippe G. Lefloch Cristinel Mardare Sorin Mardare
Assuming minimal regularity assumptions on the data, we revisit the classical problem of finding isometric immersions into the Minkowski spacetime for hypersurfaces of a Lorentzian manifold. Our approach encompasses metrics having Sobolev regularity and Riemann curvature defined in the distributional sense, only. It applies to timelike, spacelike, or null hypersurfaces with arbitrary signature that possibly changes from point to point.
keywords: Lorentzian manifold Minkowski spacetime isometric embedding general hypersurface

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