Let be an arbitrary subset of (not necessarily bounded) and , be functions. We provide necessary and sufficient conditions for the -jet to have an extension with convex and . Additionally, if is bounded we can take so that . As an application we also solve a similar problem about finding convex hypersurfaces of class with prescribed normals at the points of an arbitrary subset of .
"Global geometry and $C^1$ convex extensions of 1-jets." Anal. PDE 12 (4) 1065 - 1099, 2019. https://doi.org/10.2140/apde.2019.12.1065