Mathematical Sciences: Conformally Invariant Variational Problems

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The research entails considering problems concerning conformally equivalent metrics on classes of Riemannian manifolds, classes of spectral invariants of metrics and conformally invariant energy functions of maps. Related to these are m-powers of the energy density of maps between Riemannian manifolds. Extremals of these integrated densities lead to the notion of harmonic maps, generalizing the case m=1.