arXiv subjects
Publications and source records attributed to 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 $σ_2$ equation in domains in $\mathbb C^n,\ n\geq 2$. As a by-product we sharpen the regularity threshold of the counterexamples obtained by Li and Qiu in the real case.
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 complex torus and use it to prove a conditional statement about uniqueness of solutions to the $g$-Monge-Ampère equation.
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 transportation.
The aim of this note is to describe the geometry of $\mathbb{C}^2$ equipped with a Kähler metric defined by Warren. It is shown that with that metric $\mathbb{C}^2$ is a flat manifold. Explicit formulae for geodesics and volume of geodesic ball are also computed. Finally, a family of similar flat metrics is constructed.