2022/09/23 by Gruber, Anthony, Pampano, Alvaro, Toda, Magdalena
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2209.11597
For p∈ℝ, we show that non-circular closed p-elastic curves in \mathbbS2 exist only when p=2, in which case they are classical elastic curves, or when p∈(0,1). In the latter case, we prove that for every pair of relatively prime natural numbers n and m satisfying m<2n<√(2) m, there exists a closed spherical p-elastic curve with non-constant curvature which winds around a pole n times and closes up in m periods of its curvature. Further, we show that all closed spherical p-elastic curves for p∈(0,1) are unstable as critical points of the p-elastic energy.