Summary: The Gršotzsch Problem in Higher Dimensions
Department of Mathematics, Syracuse University, 215 Carnegie Hall,
13244-1150 Syracuse, NY, USA (e-mail: email@example.com )
December 12, 2006
An extension of Gršotzsch 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 general-
ized distortion functions is stated.
Keywords: Gršotzsch Problem, distortion function, polyconvex, extremal map-
pings, calculus of variations.
Mathematics Subject Classification (2000): 30C35, 30C65, 30C70
The purpose of this paper is to extend the Gršotzsch Problem in the plane to higher
dimensions (see below or cf.  for formulation of the problem). This elaboration
is obtained for a wide class of polyconvex energy integrals under certain conditions
imposed on them. The motivation for our work comes from recent developments in the
theory of mappings with integrable distortion  - a promissing, dynamically growing
branch of the calculus of variations.