Ricci flow on K\"ahler-Einstein manifolds

In our previous paper math.DG/0010008, we develop some new techniques in attacking the convergence problems for the K\"ahler Ricci flow. The one of main ideas is to find a set of new functionals on curvature tensors such that the Ricci flow is the gradient like flow of these functionals. We successfully find such functionals in case of Kaehler manifolds. On K\"ahler-Einstein manifold with positive scalar curvature, if the initial metric has positive bisectional curvature, we prove that these functionals have a uniform lower bound, via the effective use of Tian's inequality. Consequently, we prove the following theorem: Let $M$ be a K\"ahler-Einstein manifold with positive scalar curvature. If the initial metric has nonnegative bisectional curvature and positive at least at one point, then the K\"ahler Ricci flow will converge exponentially fast to a K\"ahler-Einstein metric with constant bisectional curvature. Such a result holds for K\"ahler-Einstein orbifolds.Comment: 49 pages. This is a revised version. Sections 4 and 5 are simplified and streamline

Strongly Coupled Inflaton

We continue to investigate properties of the strongly coupled inflaton in a setup introduced in arXiv:0807.3191 through the AdS/CFT correspondence. These properties are qualitatively different from those in conventional inflationary models. For example, in slow-roll inflation, the inflaton velocity is not determined by the shape of potential; the fine-tuning problem concerns the dual infrared geometry instead of the potential; the non-Gaussianities such as the local form can naturally become large.Comment: 12 pages; v3, minor revision, comments and reference added, JCAP versio