Singularities of axially symmetric time-like minimal submanifolds in Minkowski space

DOI10.1142/S0219891618500017zbMath1391.35011arXiv1607.06846OpenAlexW3102434771MaRDI QIDQ4609434

Willie Wai Yeung Wong

Publication date: 29 March 2018

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

Full work available at URL: https://arxiv.org/abs/1607.06846

zbMATH Keywords

singularity formationmembrane equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Analyticity in context of PDEs (35A20) Blow-up in context of PDEs (35B44) Second-order quasilinear hyperbolic equations (35L72) Axially symmetric solutions to PDEs (35B07)

Related Items

Embeddedness of timelike maximal surfaces in \((1 + 2)\)-Minkowski space, The time-like minimal surface equation in Minkowski space: low regularity solutions, GLOBAL NEARLY-PLANE-SYMMETRIC SOLUTIONS TO THE MEMBRANE EQUATION

Cites Work

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• Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space
• Closure and convexity results for closed relativistic strings
• The formation of shocks in 3-dimensional fluids.
• Kinks and the minimal surface equation in Minkowski space
• Lectures on nonlinear hyperbolic differential equations
• Stable shock formation for nearly simple outgoing plane symmetric waves
• Defects in semilinear wave equations and timelike minimal surfaces in Minkowski space
• The null condition for quasilinear wave equations in two space dimensions, II
• On smoothness of timelike maximal cylinders in three-dimensional vacuum spacetimes
• Mean Curvature Flow in Higher Codimension: Introduction and Survey
• TIMELIKE MINIMAL SUBMANIFOLDS OF GENERAL CO-DIMENSION IN MINKOWSKI SPACE TIME
• Global solutions of nonlinear hyperbolic equations for small initial data
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Formation of singularities in one-dimensional nonlinear wave propagation
• Topology of cosmic domains and strings
• A remark on global existence for small initial data of the minimal surface equation in Minkowskian space time
• Global existence for the minimal surface equation on ℝ^{1,1}
• Hypersurfaces in Minkowski space with vanishing mean curvature
• Relativistic membranes
• On the regularity of timelike extremal surfaces
• The null condition for quasilinear wave equations in two space dimensions. I