PreprintarXiv licencearXiv
On the strict approximation of currents and space-time trajectories
Abstract
This work establishes a wide variety of strict approximation results for space-time trajectories, a class of space-time currents that are used to model the evolution of dislocations in crystalline materials. In particular, we introduce a strict-type notion of convergence which respects quantities associated with geometric transport phenomena and prove approximation results in this topology. These results build on the classical strict approximation results for normal and integral currents developed by Federer and Fleming, which we also review and refine.
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BibTeX
@misc{bonicatto2026strict,
title = {{On the strict approximation of currents and space-time trajectories}},
author = {Paolo Bonicatto and Filip Rindler and Harry Turnbull},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29981},
eprint = {2610.29981},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29981},
}
RIS
TY - UNPB
TI - On the strict approximation of currents and space-time trajectories
AU - Paolo Bonicatto
AU - Filip Rindler
AU - Harry Turnbull
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29981
UR - https://arxiv.org/abs/2610.29981
AB - This work establishes a wide variety of strict approximation results for space-time trajectories, a class of space-time currents that are used to model the evolution of dislocations in crystalline materials. In particular, we introduce a strict-type notion of convergence which respects quantities associated with geometric transport phenomena and prove approximation results in this topology. These results build on the classical strict approximation results for normal and integral currents developed by Federer and Fleming, which we also review and refine.
ER -