Mathematical Sciences: Conformally Invariant Variational Problems

研究了黎曼流形上的共形等价度量、度量的谱不变量类和映射的共形不变能量函数等问题。与此相关的是黎曼流形之间映射的能量密度的m次方。这些积分密度的极值导致调和映射的概念，推广了m=1的情况。

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.