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arXiv · 2503.16898

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

Chun-Kai Lien·Chung-Jun Tsai
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Abstract

This paper explores the Bernstein problem of smooth maps $f:\mathbb{R}^4 \to \mathbb{R}^3$ whose graphs form coassociative submanifolds in $\mathbb{R}^7$. We establish a condition, expressed in terms of the second elementary symmetric polynomial of the map's slope, that ensures $f$ is affine. A corresponding result is also established for Cayley submanifolds in $\mathbb{R}^8$.

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Chun-Kai Lien, Chung-Jun Tsai. 2025-03-21. Bernstein Theorems for Calibrated Submanifolds in $\mathbb{R}^7$ and $\mathbb{R}^8$. https://arxiv.org/abs/2503.16898

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