Research project This project investigates the generalization of Cegrell's energy classes to m-subharmonic functions, as introduced by Hoang-Chinh Lu.
Cegrell's energy classes have a rich history dating back to potential theory and the works of renowned mathematicians such as Gauss, Dirichlet, and Riemann. This project investigates the generalization of Cegrell's energy classes to m-subharmonic functions, as introduced by Hoang-Chinh Lu. Our research will include the study of the complex Hessian equation, Sobolev-type inequalities, and Blocki's integrability conjecture. This may lead to advancements in the field of Metric Geometry.
