Bandyopadhyay, SaugataSil, Swarnendu2016-07-192016-07-192016-07-19201610.1051/cocv/2015007https://infoscience.epfl.ch/handle/20.500.14299/127296WOS:000375091400002We study the relation between various notions of exterior convexity introduced in [S. Bandyopadhyay, B. Dacorogna and S. Sil, J. Eur. Math. Soc. 17 (2015) 1009-1039.] with the classical notions of rank one convexity, quasiconvexity and polyconvexity. To this end, we introduce a projection map, which generalizes the alternating projection for two-tensors in a new way and study the algebraic properties of this map. We conclude with a few simple consequences of this relation which yields new proofs for some of the results discussed in [S. Bandyopadhyay, B. Dacorogna and S. Sil, J. Eur. Math. Soc. 17 (2015) 1009-1039.].Calculus of variationsrank one convexityquasiconvexitypolyconvexityexterior convexityexterior formdifferential formtext::journal::journal article::research article