The conformly invariant theory of elasticity

Let us assume that two elastic solids M and N are topolojically equivalent (homeomorphic) and Su is a solution of some boundary problem for the solid M. Taking into account these facts we want to know when it is possible to build a solution SN for N. There is no simple answer because it is necessary to take into account the metric properties of M and N. We want to modify (if it is required) the equations of the theory of elasticity and to assign the conformal weights to the field values so that the equations should be unchang~l after the eonformal change of metric. In other words, we work not with some appointed metric, but with the classes of metrics : any two metrics from the class are conformly equivalent. © 1997 Elsevier Science Ltd.