The author surveys some recent progress on the Toda system on a twodimensional surface Σ, arising in models from self-dual non-abelian Chern-Simons vortices,as well as in differential geometry. In particular, its var...The author surveys some recent progress on the Toda system on a twodimensional surface Σ, arising in models from self-dual non-abelian Chern-Simons vortices,as well as in differential geometry. In particular, its variational structure is analysed, and the role of the topological join of the barycentric sets of Σ is shown.展开更多
We review some recent results in the literature concerning existence of conformal metrics with constant Q-curvature.The problem is rather similar to the classical Yamabe problem:however辻 is characterized by a fourth-...We review some recent results in the literature concerning existence of conformal metrics with constant Q-curvature.The problem is rather similar to the classical Yamabe problem:however辻 is characterized by a fourth-order operator that might lack in general a maximum principle.For several years existence of geometrically admissible solutions was known only in particular cases.Recently;there has been instead progress in this direction for some general classes of conformal metrics.展开更多
基金supported by the project PRIN 2015 2015KB9WPT 001 and is a member of INdAM
文摘The author surveys some recent progress on the Toda system on a twodimensional surface Σ, arising in models from self-dual non-abelian Chern-Simons vortices,as well as in differential geometry. In particular, its variational structure is analysed, and the role of the topological join of the barycentric sets of Σ is shown.
基金supported by the project Geometric Variational Problems and Finanziamento a supporto della ricerca di base from Scuola Normale Superiorethe grant from MIUR Bando PRIN 2015 2015KB9WPT001
文摘We review some recent results in the literature concerning existence of conformal metrics with constant Q-curvature.The problem is rather similar to the classical Yamabe problem:however辻 is characterized by a fourth-order operator that might lack in general a maximum principle.For several years existence of geometrically admissible solutions was known only in particular cases.Recently;there has been instead progress in this direction for some general classes of conformal metrics.
