Speaker: Nguyễn Ngọc Cường (KAIST, Korea)
Time: 9:30, Wednesday, January 8, 2025
Venue: 5th floor, A6 Building
Abstract: We develop potential theory for m-subharmonic functions with respect to a Hermitian metric on a Hermitian manifold. First, we show that the complex Hessian operator is well-defined for bounded functions in this class. This allows to define the m-capacity and then showing the quasi-continuity of m-subharmonic functions. Thanks to this we derive other results parallel to those in pluripotential theory such as the equivalence between polar sets and negligible sets. The theory is then used to study the complex Hessian equation on compact Hermitian manifolds with boundary, with the right hand side of the equation admitting a bounded subsolution. This is an extension of a recent result of Collins and Picard dealing with classical solutions. This is joint work with S. Kolodziej. |
