https://neckpinch.com/authors/sebastian-hensel/New arXiv papers by Sebastian Hensel, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2404.02884arxiv:2404.02884Wed, 03 Apr 2024 00:00:00 GMTJulian Fischer, Sebastian Hensel, Alice Marveggio, Maximilian Moser — We prove a weak-strong uniqueness principle for varifold-BV solutions to planar multiphase mean curvature flow beyond a circular topology change: Assuming that there exists a classical solution with an interface that becomes increasingly circular and shrinks to a point, any varifold-BV solution with the same initial interface must coincide with it, and any varifold-BV solution with similar initial data must undergo the same type of topology change. Our result illustrates the robustness of the relative energy method for establishing weak-strong uniqueness principles for interface evolution equations, showing that it may also be applied beyond certain topological changes.Mean curvature flowWeak & singular flowsStability & uniquenessPhase fields & multiphase flows https://arxiv.org/abs/2112.11150arxiv:2112.11150Tue, 21 Dec 2021 00:00:00 GMTSebastian Hensel, Tim Laux — We study weak solutions to mean curvature flow satisfying Young's angle condition for general contact angles α∈ (0,π). First, we construct BV solutions using the Allen-Cahn approximation with boundary contact energy as proposed by Owen and Sternberg. Second, we prove the weak-strong uniqueness and stability for this solution concept. The main ingredient for both results is a relative energy, which can also be interpreted as a tilt excess.Mean curvature flowWeak & singular flowsStability & uniquenessFree boundary & capillaryPhase fields & multiphase flows https://arxiv.org/abs/2109.04233arxiv:2109.04233Thu, 09 Sep 2021 00:00:00 GMTSebastian Hensel, Tim Laux — We propose a new weak solution concept for (two-phase) mean curvature flow which enjoys both (unconditional) existence and (weak-strong) uniqueness properties. These solutions are evolving varifolds, just as in Brakke's formulation, but are coupled to the phase volumes by a simple transport equation. First, we show that, in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461, (1993)], any limit point of solutions to the Allen-Cahn equation is a varifold solution in our sense. Second, we prove that any calibrated flow in the sense of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean curvature flow - is unique in the class of our new varifold solutions. This is in sharp contrast to the case of Brakke flows, which a priori may disappear at any given time and are therefore fatally non-unique. Finally, we propose an extension of the solution concept to the multi-phase case which is at least guaranteed to satisfy a weak-strong uniqueness principle.Mean curvature flowWeak & singular flowsStability & uniquenessPhase fields & multiphase flows https://arxiv.org/abs/2108.01733arxiv:2108.01733Tue, 03 Aug 2021 00:00:00 GMTSebastian Hensel, Tim Laux — We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478v2] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions.Mean curvature flow3-manifoldsSurfacesWeak & singular flowsStability & uniquenessPhase fields & multiphase flows