Bernstein Theorems for Calibrated Submanifolds in $\mathbb {R}^7$ and $\mathbb {R}^8$

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发表日期：

2025年11月22日

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Chun-Kai Lien,
Chung-Jun Tsai

摘要

This paper explores the Bernstein problem of smooth maps $f:\mathbb {R}^4\rightarrow \mathbb {R}^3$ $f : R^{4} \to R^{3}$ whose graphs form coassociative submanifolds in $\mathbb {R}^7$ $R^{7}$ . 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 $\mathbb {R}^8$ $R^{8}$ .

Bernstein Theorems for Calibrated Submanifolds in \(\mathbb {R}^7\) and \(\mathbb {R}^8\)

摘要