A capillary problem for spacelike mean curvature flow in a cone of Minkowski space

Klingenberg, Wilhelm; Lambert, Ben; Scheuer, Julian

Abstract

Consider a convex cone in three-dimensional Minkowski space which either contains the light cone or is contained in it. This work considers mean curvature flow of a proper spacelike strictly mean convex disc in the cone which is graphical with respect to its rays. Its boundary is required to have constant intersection angle with the boundary of the cone. We prove that the corresponding parabolic boundary value problem for the graph admits a solution for all time which rescales to a self-similarly expanding solution.

Citation

Klingenberg, W., Lambert, B., & Scheuer, J. (2025). A capillary problem for spacelike mean curvature flow in a cone of Minkowski space. Journal of Evolution Equations, 25(1), Article 15. https://doi.org/10.1007/s00028-024-01045-7

• Journal Article Type: Article
• Acceptance Date: Dec 2, 2024
• Online Publication Date: Dec 21, 2024
• Publication Date: Mar 1, 2025
• Deposit Date: Jan 8, 2025
• Publicly Available Date: Jan 8, 2025
• Journal: Journal of Evolution Equations
• Print ISSN: 1424-3199
• Electronic ISSN: 1424-3202
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Issue: 1
• Article Number: 15
• DOI: https://doi.org/10.1007/s00028-024-01045-7
• Keywords: 35R35, Capillary boundary condition, Spacelike mean curvature flow, 53E10
• Public URL: https://durham-repository.worktribe.com/output/3229892