Convex and quasiconvex truncations of nonconvex functions
Classical Analysis and ODEs
2026-03-05 v1 Differential Geometry
Abstract
We consider nonconvex real valued functions whose truncations are either quasiconvex or even convex starting with a certain level. Among them, the -smooth functions whose level sets are all completely contained in the positive definite region of their Hessian matrices, starting with a certain level, are good examples of such functions. For such a function we show the injectivity of its restricted gradient to a large subset of the positive definite region of its Hessian matrices.
Keywords
Cite
@article{arxiv.2603.03516,
title = {Convex and quasiconvex truncations of nonconvex functions},
author = {Cornel Pintea},
journal= {arXiv preprint arXiv:2603.03516},
year = {2026}
}