On absolute minima of the volume and Dirichlet functionals on Riemannian manifolds (Q796821)

The paper deals with the minimum problem for functionals of the form \(D[f]=\int_{M}\sum_{i,j,\alpha,\beta}g^{ij}y_{\alpha,i}y_{\beta, j}\hat g_{\alpha \beta}d^ kx\). Here M denotes a Riemannian manifold, f: \(X\to M\), X is a smooth compact closed manifold, \(g_{ij}\) and \(\hat g{}_{\alpha \beta}\) are metric tensors on X and M respectively and \(y_ i=f_ i(x_ 1,...,x_ k)\). The paper has the character of a survey. It contains some results of other authors too. No proofs are given.