PreprintarXiv licencearXiv
Existence of closed non-planar p-elasticae
Abstract
We prove existence of closed non-planar p-elasticae for general exponents p∈ (1,∞). In particular, we show that for any p ∈ (1,∞), there exists a countable family of non-planar p-elasticae, which are realized as torus knots. This generalizes well-known results of Langer--Singer for the quadratic case p=2 to general exponents p∈ (1,∞).
Related
- Global existence and uniqueness for the planar four-velocity Broadwell model with arbitrary C1 bounded initial and boundary data in a rectangular domain
- The Eighth-Order Evolution Model for Closed Planar Curves
- Four colours are needed for closed-neighbourhood conflict-free colouring of all planar graphs
- A Counterexample to the Closed Nodal-Line Conjecture for the Third Eigenfunction of the Planar Dirichlet Laplacian
- Representation-Aware Closed-Surface Parameterization: Exact Sensitivity Analysis and Pole-Aware Planar Preconditioning
BibTeX
@misc{gruen2026existence,
title = {{Existence of closed non-planar $p$-elasticae}},
author = {Florian Gruen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02073},
eprint = {2609.02073},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02073},
}
RIS
TY - UNPB
TI - Existence of closed non-planar p-elasticae
AU - Florian Gruen
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02073
UR - https://arxiv.org/abs/2609.02073
AB - We prove existence of closed non-planar p-elasticae for general exponents p∈ (1,∞). In particular, we show that for any p ∈ (1,∞), there exists a countable family of non-planar p-elasticae, which are realized as torus knots. This generalizes well-known results of Langer--Singer for the quadratic case p=2 to general exponents p∈ (1,∞).
ER -