An extension of the Grötzsch Problem to higher dimensions is considered. The problem is formulated and proven for a subclass of polyconvex energy integrals and counterexamples in general case are given. A conjecture about the generalized distortion functions is stated.
Cite this article
Tomasz Adamowicz, The Grötzsch problem in higher dimensions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), no. 2, pp. 163–177DOI 10.4171/RLM/488