
Journal of Convex Analysis 30 (2023), No. 1, 271294 Copyright Heldermann Verlag 2023 Properties of the Level Sets of Some Products of Functions Andi Brojbeanu Faculty of Mathematics and Computer Science, BabesBolyai University, ClujNapoca, Romania andibrojbeanu014@gmail.com Cornel Pintea Faculty of Mathematics and Computer Science, BabesBolyai University, ClujNapoca, Romania cpintea@math.ubbcluj.ro [Abstractpdf] We are interested about pairs $(f,g)$ of $C^2$smooth functions $f,g:\mathbb{R}^n\longrightarrow\mathbb{R}$ with bounded ${\rm Hess}^+$ complements such that their product preserves this property as well. Recall that ${\rm Hess}^+(f)$ stands for the set of all points $p\in\mathbb{R}^n$ such that the Hessian matrix $H_p(f)$ of the $C^2$smooth function $f\colon \mathbb{R}^n\longrightarrow\mathbb{R}$ is positive definite. In this paper we consider two pairs of realvalued functions with empty ${\rm Hess}^+$ complements whose products happen to have bounded ${\rm Hess}^+$ complements. Keywords: Level curves, Lagrange multipliers, Hessian matrix, curvature. MSC: 47H05; 47H99. [ Fulltextpdf (742 KB)] for subscribers only. 