Stability of Ricci Yang–Mills flow at Einstein Yang–Mills metrics

Stability of the Ricci Yang-mills Flow at Einstein Yang-mills Metrics

Let P be a principal U(1)-bundle over a closed manifold M . On P , one can define a modified version of the Ricci flow called the Ricci Yang-Mills flow, due to these equations being a coupling of Ricci flow and the Yang-Mills heat flow. We use maximal regularity theory and ideas of Simonett concerning the asymptotic behavior of abstract quasilinear parabolic partial differential equations to st...

Kähler-Ricci flow, Kähler-Einstein metric, and K-stability

We prove the existence of Kähler-Einstein metric on a K-stable Fano manifold using the recent compactness result on Kähler-Ricci flows. The key ingredient is an algebro-geometric description of the asymptotic behavior of Kähler-Ricci flow on Fano manifolds. This is in turn based on a general finite dimensional discussion, which is interesting in its own and could potentially apply to other prob...

0 Ricci flow on Kähler - Einstein surfaces

Ricci Flow on Kähler-einstein Manifolds

Ricci Flow on Kähler-einstein Surfaces