https://neckpinch.com/authors/sven-hirsch/New arXiv papers by Sven Hirsch, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2310.08005/arxiv:2310.08005Thu, 12 Oct 2023 00:00:00 GMTSven Hirsch, Jonathan J. Zhu — We prove uniqueness of tangent cones for forced mean curvature flow, at both closed self-shrinkers and round cylindrical self-shrinkers, in any codimension. The corresponding results for mean curvature flow in Euclidean space were proven by Schulze and Colding-Minicozzi respectively. We adapt their methods to handle the presence of the forcing term, which vanishes in the blow-up limit but complicates the analysis along the rescaled flow. Our results naturally include the case of mean curvature flows in Riemannian manifolds.Mean curvature flowVolume-preserving & constrained flowsSelf-shrinkers & translatorsSingularitiesStability & uniqueness https://neckpinch.com/papers/2210.12237/arxiv:2210.12237Fri, 21 Oct 2022 00:00:00 GMTSven Hirsch — We introduce new systems of PDE on initial data sets (M,g,k) whose solutions model double-null foliations. This allows us to generalize Geroch's monotonicity formula for the Hawking mass under inverse mean curvature flow to initial data sets satisfying the dominant energy condition. We study the existence theory of these systems and give geometric applications.Mean curvature flowOther curvature flowsInverse mean curvature flowPhysics