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Geometry Colloquium
Seminar information archive ～04/22｜Next seminar｜Future seminars 04/23～
| Date, time & place | Friday 10:00 - 11:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2016/05/27
13:00-14:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Matsumoto (Osaka University)
Deformation of Einstein metrics and $L^2$ cohomology on strictly pseudoconvex domains (Japanese)
Yoshihiko Matsumoto (Osaka University)
Deformation of Einstein metrics and $L^2$ cohomology on strictly pseudoconvex domains (Japanese)
[ Abstract ]
Any bounded strictly pseudoconvex domain of a Stein manifold carries a complete Kähler-Einstein metric of negative scalar curvature, which is unique up to homothety, as shown by S. Y. Cheng and S. T. Yau. I will discuss the fact that this Cheng-Yau metric deforms into a family of Einstein metrics parametrized by partially integrable CR structures on the boundary under the assumption that the dimension is at least three. The necessary analysis on the linearized Einstein operator can be reduced to a vanishing result of the $L^2$ Dolbeault cohomology with values in the holomorphic tangent bundle.
Any bounded strictly pseudoconvex domain of a Stein manifold carries a complete Kähler-Einstein metric of negative scalar curvature, which is unique up to homothety, as shown by S. Y. Cheng and S. T. Yau. I will discuss the fact that this Cheng-Yau metric deforms into a family of Einstein metrics parametrized by partially integrable CR structures on the boundary under the assumption that the dimension is at least three. The necessary analysis on the linearized Einstein operator can be reduced to a vanishing result of the $L^2$ Dolbeault cohomology with values in the holomorphic tangent bundle.
