Helein, Frédéric Inégalité isopérimétrique et calibration. (Isoperimetric inequality and calibration). (French) Zbl 0830.49029 Ann. Inst. Fourier 44, No. 4, 1211-1218 (1994). Summary: We show that the isoperimetric inequality for a domain in the Euclidean plane, the two-dimensional sphere, or the two-dimensional hyperbolic space, may be obtained using a calibration. MSC: 49Q20 Variational problems in a geometric measure-theoretic setting Keywords:isoperimetric inequalities; calibrations; null Lagrangians PDF BibTeX XML Cite \textit{F. Helein}, Ann. Inst. Fourier 44, No. 4, 1211--1218 (1994; Zbl 0830.49029) Full Text: DOI Numdam EuDML References: [1] M. BERGER, Géométrie, chapitre 12, Tome 2, Nathan, 1990. [2] W. BLASCHKE, Kreis und kugel, Chelsea. · Zbl 0153.23601 [3] H. FEDERER, Geometric measure theory, Springer-Verlag, New York, 1969. · Zbl 0176.00801 [4] R. HARVEY, H.B. LAWSON, Calibrated geometries, Acta Mathematica, 148 (1982), 47-157. · Zbl 0584.53021 [5] R. OSSERMAN, Bonnensen-style isoperimetric inequalities, Amer. Math. Monthly, 86 (1979), 1-29. · Zbl 0404.52012 [6] R. OSSERMAN, The isoperimetric inequality, Bull. Amer. Math. Soc., 84 (1978), 1182-1238. · Zbl 0411.52006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.