Soliton-type metrics and Kähler–Ricci flow on symplectic quotients
-
Gabriele La Nave
und
Gang Tian
Abstract
In this paper, we first show an interpretation of the Kähler–Ricci flow on a manifold X as an exact elliptic equation of Einstein type on a manifold M of which X is one of the (Kähler) symplectic reductions via a (non-trivial) torus action. There are plenty of such manifolds (e.g. any line bundle on X will do). Such an equation is called V-soliton equation, which can be regarded as a generalization of Kähler–Einstein equations or Kähler–Ricci solitons. As in the case of Kähler–Einstein metrics, we can also reduce the V-soliton equation to a scalar equation on Kähler potentials, which is of Monge–Ampère type. We then prove some preliminary results towards establishing existence of solutions for such a scalar equation on a compact Kähler manifold M. One of our motivations is to apply the interpretation to studying finite time singularities of the Kähler–Ricci flow.
© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Quiver Hecke superalgebras
- On a p-adic invariant cycles theorem
- On the Chow motive of an abelian scheme with non-trivial endomorphisms
- Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components
- Soliton-type metrics and Kähler–Ricci flow on symplectic quotients
- On semi-continuity problems for minimal log discrepancies
- The Haagerup property for locally compact quantum groups
- The spt-crank for ordinary partitions
Artikel in diesem Heft
- Frontmatter
- Quiver Hecke superalgebras
- On a p-adic invariant cycles theorem
- On the Chow motive of an abelian scheme with non-trivial endomorphisms
- Dirichlet heat kernel estimates for subordinate Brownian motions with Gaussian components
- Soliton-type metrics and Kähler–Ricci flow on symplectic quotients
- On semi-continuity problems for minimal log discrepancies
- The Haagerup property for locally compact quantum groups
- The spt-crank for ordinary partitions
