Bernstein Theorems for Calibrated Submanifolds in ℝ⁷ and ℝ⁸

2025/03/21 by Chun-Kai Lien, Lien, Chun-Kai, Chung-Jun Tsai +1
Mathematics · Physics and Astronomy · #35J60 #49Q05 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Primary 53C38 #Secondary 53A10

paper · pdf · doi:10.48550/arxiv.2503.16898

openalex publication_date 2025/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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 ℝ⁸.

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