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Uniform W2,m approximation of almost isometric maps
Abstract
This paper shows that an almost-isometric Sobolev map from a Lipschitz subset of an oriented manifold M into another oriented manifold N can be approximated by a map of class C1,α, with a universal bound on the W2,m norm, for any m∈(1,∞). This, in turn, implies a universal bound on the C1,α seminorm. The W1,p distance of the approximation from the original map is controlled in terms of the Lp-deviation from being an isometry, with the optimal scaling. The manifolds M and N are assumed to be compact, oriented and have equal dimension; M may have a boundary.
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BibTeX
@misc{conti2026uniform,
title = {{Uniform $W^2,m$ approximation of almost isometric maps}},
author = {Sergio Conti and Georg Dolzmann and Stefan Müller},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37249},
eprint = {2609.37249},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37249},
}
RIS
TY - UNPB
TI - Uniform W^2,m approximation of almost isometric maps
AU - Sergio Conti
AU - Georg Dolzmann
AU - Stefan Müller
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37249
UR - https://arxiv.org/abs/2609.37249
AB - This paper shows that an almost-isometric Sobolev map from a Lipschitz subset of an oriented manifold M into another oriented manifold N can be approximated by a map of class C^1,α, with a universal bound on the W^2,m norm, for any m∈(1,∞). This, in turn, implies a universal bound on the C^1,α seminorm. The W^1,p distance of the approximation from the original map is controlled in terms of the L^p-deviation from being an isometry, with the optimal scaling. The manifolds M and N are assumed to be compact, oriented and have equal dimension; M may have a boundary.
ER -