Communications in Analysis and Geometry

Volume 28 (2020)

Number 6

Total $p$-powered curvature of closed curves and flat-core closed $p$-curves in $S^2(G)$

Pages: 1451 – 1487

DOI: https://dx.doi.org/10.4310/CAG.2020.v28.n6.a6

Authors

Naoki Shioji (Department of Mathematics, Faculty of Engineering, Yokohama National University, Yokohama, Japan)

Kohtaro Watanabe (Department of Computer Science, National Defense Academy, Yokosuka, Japan)

Abstract

We consider a variational problem of $p$-elastic curves in two-dimensional sphere. We give its first variation formula, and in two-dimensional sphere, we give a realization of a solution which satisfies that the first variation formula is zero. We also show the existence of a flat-core, closed $p$-elastic curve.

Full Text (PDF format)

The work of Naoki Shioji was partially supported by the Grant-in-Aid for Scientific Research (C) (No. 26400160) from Japan Society for the Promotion of Science.

The work of Kohtaro Watanabe was partially supported by the Grant-in-Aid for Scientific Research (C) (No. 15K04973) from Japan Society for the Promotion of Science.

Received 2 June 2015

Accepted 8 February 2018

Published 2 December 2020