Exterior convexity and classical calculus of variations (Q2808047)

The authors study the relation between various notions of exterior convexity introduced in [\textit{S. Bandyopadhyay} et al., J. Eur. Math. Soc. (JEMS) 17, No. 4, 1009--1039 (2015; Zbl 1317.49015)] with the classical notions of rank one convexity, quasiconvexity and polyconvexity. The main idea is to introduce a suitable projection map, which generalizes the alternating projection for two-tensors and to study the algebraic properties of this map. The properties of the projection map permit to express the connection of the different notions in an explicit and attractive way.