The ∞-elastica problem on a Riemannian manifold

Ed Gallagher; Roger Moser

doi:10.1007/s12220-023-01281-2

The ∞-elastica problem on a Riemannian manifold

Ed Gallagher, Roger Moser

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (SciVal)

Abstract

We consider the following problem: on any given complete Riemannian manifold (M,g), among all curves which have fixed length as well as fixed end-points and tangents at the end-points, minimise the L∞ norm of the curvature. We show that the solutions of this problem, as well as a wider class of curves, must satisfy a second order ODE system. From this system we obtain some geometric information about the behaviour of the curves.

Original language	English
Article number	226
Number of pages	26
Journal	Journal of Geometric Analysis
Volume	33
Issue number	7
DOIs	https://doi.org/10.1007/s12220-023-01281-2
Publication status	Published - 3 May 2023

Bibliographical note

Ed Gallagher is grateful for being funded by a studentship from the EPSRC, project reference 2446338.

Keywords

Curvature
Elastica
L variational problem
Riemannian manifold

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-023-01281-2Licence: CC BY

https://arxiv.org/abs/2202.07407

Cite this

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The ∞-elastica problem on a Riemannian manifold

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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