TIMELIKE MINIMAL SUBMANIFOLDS OF GENERAL CO-DIMENSION IN MINKOWSKI SPACE TIME

DOI10.1142/S0219891606000963zbMath1108.35118arXivmath/0512036OpenAlexW2069662328MaRDI QIDQ3426968

Paul T. Allen, Lars Andersson, James A. Isenberg

Publication date: 14 March 2007

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0512036

zbMATH Keywords

local and global existencestability of solutions of nonlinear hyperbolic PDEstimelike minimal submanifolds

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (16)

Long time existence for the bosonic membrane in the light cone gauge ⋮ Quasi-periodic relativistic strings in the Minkowski space \(\mathbb{R}^{1+n}\) ⋮ Embeddedness of timelike maximal surfaces in \((1 + 2)\)-Minkowski space ⋮ GLOBAL NEARLY-PLANE-SYMMETRIC SOLUTIONS TO THE MEMBRANE EQUATION ⋮ Singularities of axially symmetric time-like minimal submanifolds in Minkowski space ⋮ Global existence of timelike minimal surface of general co-dimension in Minkowski space time ⋮ The effective theory of strings ⋮ Boundedness of the total energy of relativistic membranes evolving in a curved spacetime ⋮ Global regularity for the minimal surface equation in Minkowskian geometry ⋮ Global existence of smooth solutions to relativistic string equations in Schwarzschild space-time for small initial data ⋮ Spherical symmetric solutions for the motion of relativistic membranes in the Schwarzschild spacetime ⋮ Stability of traveling wave for the relativistic string equation in de Sitter spacetime ⋮ On indefinite special Lagrangian submanifolds in indefinite complex Euclidean spaces ⋮ Harmonic coordinates in the string and membrane equations ⋮ Global weak and smooth solutions of the equation for timelike extremal surface in Minkowski space ⋮ Global existence of smooth solution to relativistic membrane equation with large data

Cites Work

• A better conformal Bernstein's theorem
• Weighted L∞ and L1 estimates for solutions to the classical wave equation in three space dimensions
• Almost global existence for quasilinear wave equations in three space dimensions
• A remark on global existence for small initial data of the minimal surface equation in Minkowskian space time
• Hypersurfaces in Minkowski space with vanishing mean curvature
• On the lifespan of solutions of nonlinear wave equations with small initial data

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