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Total $p$-powered curvature of closed curves and flat-core closed $p$-curves in $S^2(G)$
Communications in Analysis and Geometry  (IF0.736),  Pub Date : 2020-12-02, DOI: 10.4310/cag.2020.v28.n6.a6
Naoki Shioji, Kohtaro Watanabe

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.