3 papers
math.AP2024
Very weak solutions of quadratic Hessian equations
Sławomir Dinew, Szymon Myga
We extend the methods of Lewicka - Pakzad, Székelyhidi - Cao and Li - Qiu to study the notion of very weak solutions to the complex equation in domains in $\mathbb C^n,\ n\ge…
math.CV2021
On the conditional measures on the orbits of the complex torus
Szymon Myga
We explore the structure of invariant measures on compact Kähler manifolds with Hamiltonian torus actions. We derive the formula for conditional measures on the orbits of the compl…
math.AP2019
Optimal transport on completely integrable toric manifolds
Szymon Myga
We show that existence and uniqueness of solutions to transported Monge-Ampere problem on complex compact toric manifold follows easily from the real theory of optimal transportati…