Locally convex extensions of -jets
Daniel Azagra
Universidad Complutense de Madrid, Spain
![Locally $C^{1,1}$ convex extensions of $1$-jets cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rmi-volume-38-issue-1.png&w=3840&q=90)
Abstract
Let be an arbitrary subset of , and let , be given functions. We provide necessary and sufficient conditions for the existence of a convex function such that and on . We give a useful explicit formula for such an extension , and a variant of our main result for the class , where is a modulus of continuity. We also present two applications of these results, concerning how to find convex hypersurfaces with prescribed tangent hyperplanes on a given subset of , and some explicit formulas for (not necessarily convex) extensions of -jets.
Cite this article
Daniel Azagra, Locally convex extensions of -jets. Rev. Mat. Iberoam. 38 (2022), no. 1, pp. 131–174
DOI 10.4171/RMI/1274