https://neckpinch.com/authors/wilhelm-klingenberg/New arXiv papers by Wilhelm Klingenberg, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2304.05702/arxiv:2304.05702Wed, 12 Apr 2023 00:00:00 GMTBrendan Guilfoyle, Wilhelm Klingenberg — It is proven that a definite graphical rotationally symmetric line congruence evolving under mean curvature flow with respect to the neutral Kaehler metric in the space of oriented lines of Euclidean 3-space, subject to suitable Dirichlet and Neumann boundary conditions, converges to a maximal surface. When the Neumann condition implemented is that the flowing disc be holomorphic at the boundary, it is proven that the flow converges to a holomorphic disc. This is extended to the flow of a family of discs with boundary lying on a fixed rotationally symmetric line congruence, which is shown to converge to a filling by maximal surfaces. Moreover, if the family is required to be holomorphic at the boundary, it is shown that the flow converges to the Bishop filling by holomorphic discs of an isolated complex point of Maslov index 2.Mean curvature flowKähler geometryBoundaries & non-compactFree boundary & capillaryRotational symmetry & warped products https://neckpinch.com/papers/2304.02414/arxiv:2304.02414Wed, 05 Apr 2023 00:00:00 GMTWilhelm Klingenberg, Ben Lambert, Julian Scheuer — Consider a convex cone in three-dimensional Minkowski space which either contains the lightcone 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.Mean curvature flow3-manifoldsFree boundary & capillaryPhysics