Hyperbolicity of the time-like extremal surfaces in minkowski spaces

2017/06/15 by Xianglong Duan, Duan, Xianglong
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1706.04768

openalex publication_date 2017/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, it is established, in the case of graphs, that time-like extremal surfaces of dimension 1+n in the Minkowski space of dimension 1+n+m can be described by a symmetric hyperbolic system of PDEs with the very simple structure (reminiscent of the inviscid Burgers equation)∂_t W + ∑_j=1ⁿ A_j(W)∂_x_j W =0, W: (t,x)∈ℝ¹⁺ⁿ→ W(t,x)∈ℝ^n+m+\binomm+nn,where each A_j(W) is just a (n+m+\binomm+nn)×(n+m+\binomm+nn) symmetric matrix dependinglinearly on W.

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