Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Trudinger, Neil S., Wang, Xu-Jia
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220978753