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Blow-ups of minimal surfaces in the Heisenberg group

2024/07/07 by Yonghao Yu, Yu, Yonghao
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2407.05513

openalex publication_date 2024/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we revise Monti's results on the blow-ups of H-perimeter minimizing sets in ℍn. Monti demonstrated that the Lipschitz approximation of the blow-up, after rescaling by the square root of the excess, converges to a limit function for n ≥ 2. However, the partial differential equation he derived for this limit function φ through contact variation is incorrect. Instead, the correct equation is that the horizontal Laplacian of the limit function φ is independent of the coordinate y1 and solves equation 1 weakly.

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