Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space II

2024/10/23 by Shanshan Li, Li, Shanshan, Jisong Lv +3
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geophysics and Gravity Measurements

paper · pdf · doi:10.48550/arxiv.2410.17794

openalex publication_date 2024/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the mean curvature flow of entire Lagrangian graphs with initial data in the pseudo-Euclidean space, which is related to the special Lagrangian parabolic equation. We show that the parabolic equation \eqref11 has a smooth solution u(x,t) for three corresponding nonlinear equations between the Monge-Amp\graveere type equation(τ=0) and the special Lagrangian parabolic equation(τ=\fracπ2). Furthermore, we get the bound of D^lu, l=\3,4,5,⋯\ for τ=\fracπ4 and the decay estimates of the higher order derivatives when 0<τ<\fracπ4 and \fracπ4<τ<\fracπ2. We also prove that u(x,t) converges to smooth self-expanding solutions of \eqref12.

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