PreprintCC BY-NC-ND 4.0arXiv
The higher dimensional affine Bernstein and Plateau problems
Abstract
In our previous papers [33, 34], we established the affine Bernstein theorem and proved the interior regularity for the affine Plateau problem in two dimensions. In this paper, we prove the interior regularity for the affine Plateau problem in all dimensions and present a smooth counterexample to the affine Bernstein problem in dimensions ten and higher. We also prove an affine Bernstein theorem in all dimensions under a growth condition.
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BibTeX
@misc{trudinger2026higher,
title = {{The higher dimensional affine Bernstein and Plateau problems}},
author = {Neil S. Trudinger and Xu-Jia Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09385},
eprint = {2610.09385},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09385},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The higher dimensional affine Bernstein and Plateau problems
AU - Neil S. Trudinger
AU - Xu-Jia Wang
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09385
UR - https://arxiv.org/abs/2610.09385
AB - In our previous papers [33, 34], we established the affine Bernstein theorem and proved the interior regularity for the affine Plateau problem in two dimensions. In this paper, we prove the interior regularity for the affine Plateau problem in all dimensions and present a smooth counterexample to the affine Bernstein problem in dimensions ten and higher. We also prove an affine Bernstein theorem in all dimensions under a growth condition.
ER -