2025/12/22 by Klaus Deckelnick, Deckelnick, Klaus, Hans-Christoph Grunau +7
Mathematics · #53C44 #Analysis of PDEs (math.AP) #Attraction #Boundary (topology) #Conjecture #Descent (aeronautics) #Differential Geometry (math.DG) #FOS: Mathematics #Flow (mathematics) #Flow line #Geometric Analysis and Curvature Flows #Gradient descent #Line (geometry) #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations
paper · open access · doi:10.48550/arxiv.2512.19015
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28
The free boundary free elastic flow is the steepest descent gradient flow for the elastic energy of curves meeting parallel lines perpendicularly. In this article we prove that the straight line has, measured in Euler's scale-invariant bending energy, a basin of attraction at least to the level 1.9615 π. We show that our method of proof cannot be pushed to the previously conjectured level 2π, and in addition present numerical evidence that this conjecture may in fact be false.