A nonlinear Fubini-Lebesgue theorem identifies L^p curves in nonlinear Lebesgue spaces with maps into spaces of L^p curves, yielding pointwise length, curvature bounds, and speed for absolutely continuous curves.
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Nonlinear Lebesgue spaces: Curves and geometry
A nonlinear Fubini-Lebesgue theorem identifies L^p curves in nonlinear Lebesgue spaces with maps into spaces of L^p curves, yielding pointwise length, curvature bounds, and speed for absolutely continuous curves.