H-functional and Matsushima type decomposition theorem

The H-functional characterizes K\"ahler-Ricci solitons as its critical points, and also plays an important role of the existence problem for K\"ahler-Einstein metrics. In this paper we prove the Hessian formula for the H-functional at its critical points, and use this to obtain a new proof of Matsushima type decomposition theorem for holomorphic vector fields on Fano manifolds admitting K\"ahler-Ricci solitons.Comment: Typos are fixed. References are adde

Effect of three-pion unitarity on resonance poles from heavy meson decays

We study the final state interaction in 3-pion decay of meson resonances at the Excited Baryon Analysis Center (EBAC) of JLab. We apply the dynamical coupled-channels formulation which has been extensively used by EBAC to extract N* information. The formulation satisfies the 3-pion unitarity condition which has been missed in the existing works with the isobar models. We report the effect of the 3-pion unitarity on the meson resonance pole positions and Dalitz plot.Comment: 4 pages, 4 figures, Contribution to the proceedings of International conference on the structure of baryons (BARYONS'10), Osaka, Japan, Dec. 7-11, 201