5 papers
Hessian operators, null Lagrangians and the integral comparison principle
Sławomir Dinew, Szymon Myga, Marcin Sroka
We investigate the conditions under which a Hessian operator satisfies the integral comparison principle. We establish a rather unexpected connection with the notion of a null Lagr…
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…
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…
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…
The geometry of equipped with Warren's metric
Szymon Myga
The aim of this note is to describe the geometry of equipped with a Kähler metric defined by Warren. It is shown that with that metric is a flat manif…