https://neckpinch.com/authors/johannes-ruf/New arXiv papers by Johannes Ruf, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2003.13611/arxiv:2003.13611Mon, 30 Mar 2020 00:00:00 GMTMartin Larsson, Johannes Ruf — We study the following question: What is the largest deterministic amount of time T_* that a suitably normalized martingale X can be kept inside a convex body K in ℝ^d? We show, in a viscosity framework, that T_* equals the time it takes for the relative boundary of K to reach X(0) as it undergoes a geometric flow that we call (positive) minimum curvature flow. This result has close links to the literature on stochastic and game representations of geometric flows. Moreover, the minimum curvature flow can be viewed as an arrival time version of the Ambrosio–Soner codimension-(d-1) mean curvature flow of the 1-skeleton of K. Our results are obtained by a mix of probabilistic and analytic methods.Mean curvature flowOther curvature flows