KASS-seminarium

Abstrakt finns enbart på engelska: Using Monge-Ampère equations to obtain auxiliary functions, Guo-Phong-Tong proved $L^\infty$ esimates for Monge-Ampère and Hessian equations on compact Kähler manifolds. These estimates are uniform in a bounded subset of the Kähler cone, provided certain cohomological constants - involving the volume - are bounded. This makes the estimates especially useful for dealing with degenerations to big and nef classes. However, if the limiting class is only nef and of numerical dimension $1<k<n$, the cohomological constant is not under control. In this case, we propose to adapt the technique using auxiliary Hessian equations. I will explain the modifications needed and some proof-of-concept results.