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

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 co...

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Veröffentlicht in:	Journal of evolution equations 2025-03, Vol.25 (1), Article 15
Hauptverfasser:	Klingenberg, Wilhelm, Lambert, Ben, Scheuer, Julian
Format:	Artikel
Sprache:	eng
Schlagworte:	Boundary value problems Capillary flow Curvature Minkowski space Three dimensional flow
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container_title	Journal of evolution equations
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creator	Klingenberg, Wilhelm Lambert, Ben Scheuer, Julian
description	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.
doi_str_mv	10.1007/s00028-024-01045-7
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subjects	Boundary value problems Capillary flow Curvature Minkowski space Three dimensional flow
title	A capillary problem for spacelike mean curvature flow in a cone of Minkowski space
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