Fields Geometric Analysis Colloquium
by Nicholas McCleerey (Purdue University)
Recently, Y. Xu has shown Holder regularity for weak solutions to complex $m$-Hessian equations on compact Hermitian manifolds. We present a new, effective proof of this result, using a two-point maximum principle argument. We then demonstrate how to go further, and obtain optimal Holder regularity on compact Kahler manifolds, when the right-hand side is bounded and $m\geq 3$; this is new even for the complex Monge-Ampere equation. For $m=2$ or right-hand sides in $L^p$, the method is nearly optimal, giving all Holder exponents below the best possible one.
https://www.fields.utoronto.ca/activities/26-27/geometric-analysis-colloquium
