94 citations · 266 across the 30 of their papers we have counts for
39 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…
Three Bernstein type theorems for hypersurfaces with zero Gaussian curvature
Slawomir Dinew, Mengru Guo, Heming Jiao
In this paper, we prove Bernstein type theorems for entire convex graphical hypersurfaces with zero Gaussian curvature in both Euclidean and Minkowski context. A supplementary exam…
-Pseudo-effectivity and a Monge-Ampère-Type Equation for Forms of Positive Degree
Sławomir Dinew, Dan Popovici
Given an -dimensional compact Kähler manifold, we continue our study of -positivity in two ways. We first propose generalisations of the notions of pseudo-effective and big B…
-Positivity and Regularisation
Sławomir Dinew, Dan Popovici
Starting from the notion of -plurisubharmonic function introduced recently by Dieu and studied, in particular, by Harvey and Lawson, we consider -(semi-)positive -cu…
A priori estimates for the complex Monge-Ampère equation after Krylov
Sławomir Dinew, Marcin Sroka
We establish an analytic proof for the Krylov estimates for solutions of degenerate complex Monge-Ampère equation. We also provide an analytic proof of the Bedford-Taylor…
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…