Year: 2026
Type: preprint
Abstract: 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 Lagrangian from the calculus of variations. Under mild conditions we obtain a complete classification, showing that the only operators for which the integral comparison principle holds are linear combinations of $k$-Hessians and, in the homogeneous case, precisely the $k$-Hessians themselves. An analogous result is established for the complex Hessian operator, revealing in particular substantial obstructions to the development of a genuine pluripotential theory for the $\mathcal{J}$-equation.
Source: arXiv (Cornell University)
Authors: Dinew, Sławomir, Myga, Szymon, Sroka, Marcin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220660628