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Our main result gives an improved bound on the filling areas of curves in Banach spaces which are not closed geodesics. As applications we show rigidity of Pu’s classical systolic inequality and investigate the isoperimetric constants of normed spaces. The latter has further applications concerning the regularity of minimal surfaces in Finsler manifolds.
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Paul Creutz, Rigidity of the Pu inequality and quadratic isoperimetric constants of normed spaces. Rev. Mat. Iberoam. 38 (2022), no. 3, pp. 705–729DOI 10.4171/RMI/1309