Extension of Convex Function

2012/07/04 by Yan, Min · 3 citations
#26B25 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1207.0944

Abstract

We study the local and global versions of the convexity, which is closely related to the problem of extending a convex function on a non-convex domain to a convex function on the convex hull of the domain and beyond the convex hull. We also give the parallel results for the convexity defined by positive definite Hessian.

Cited by

• Optimal asymptotic expansion of entire solutions to Monge-Ampère equation with C^α perturbed periodic data
• Folded optimal transport and its application to separable quantum optimal transport
• On the Kantorovich contraction of Markov semigroups

Related

• On extensions of d.c. functions and convex functions
• An extension problem for convex functions
• On a convexity problem
• Searching for, and quantifying, non-convexity of functions
• On convex functions and the finite element method