Embeddedness and graphicality of the elastic flow for complete curves

2025/08/26 by Miura, Tatsuya, Rupp, Fabian
#49Q10 (secondary) #53A04 #53E40 (primary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.18979

Abstract

We study positivity-preserving properties for the elastic flow of non-compact, complete curves in Euclidean space. Despite the fact that the canonical elastic energy is infinite in this context, we extend our recent work based on the adapted elastic energy to derive nontrivial optimal thresholds for maintaining planar embeddedness and graphicality, respectively. We also obtain a new Li--Yau type inequality for complete planar curves.

Citations

• A new energy method for shortening and straightening complete curves
• Migrating elastic flows II
• Uniqueness and minimality of Euler's elastica with monotone curvature
• Curve shortening-straightening flow for non-closed planar curves with infinite length

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