PreprintCC BY 4.0arXiv
Hyperrigidity and convexity in two variables
Abstract
We extend Brown's one-variable rigidity theorem to strictly convex functions of two variables under a regularity assumption. Let K⊂ℝ2 be nonempty, compact, and convex, and let f be real-valued, strictly convex on K, and of class C2 on a neighbourhood of K. We prove that the generating set {x1,x2,f} is hyperrigid in C(K).
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BibTeX
@misc{pietrzycki2026hyperrigidity,
title = {{Hyperrigidity and convexity in two variables}},
author = {Paweł Pietrzycki},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03716},
eprint = {2611.03716},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03716},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hyperrigidity and convexity in two variables
AU - Paweł Pietrzycki
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.03716
UR - https://arxiv.org/abs/2611.03716
AB - We extend Brown's one-variable rigidity theorem to strictly convex functions of two variables under a regularity assumption. Let K⊂ℝ^2 be nonempty, compact, and convex, and let f be real-valued, strictly convex on K, and of class C^2 on a neighbourhood of K. We prove that the generating set {x_1,x_2,f} is hyperrigid in C(K).
ER -