Bernstein Theorems for Calibrated Submanifolds in $$\mathbb {R}^7$$ and $$\mathbb {R}^8$$
Journal
The Journal of Geometric Analysis
Journal Volume
36
Journal Issue
1
ISSN
1050-6926
1559-002X
Date Issued
2025-11-22
Author(s)
Lien, Chun-Kai
Abstract
This paper explores the Bernstein problem of smooth maps f:R4→R3 whose graphs form coassociative submanifolds in R7. We establish a condition, expressed in terms of its 2-dilations, that ensures f is affine. To the best of our current knowledge, our theorem achieves the minimal deficiency regarding the Lawson–Osserman cone. A corresponding result is also established for Cayley submanifolds in R8.
Publisher
Springer Science and Business Media LLC
Type
journal article