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2019 Global geometry and $C^1$ convex extensions of 1-jets
Daniel Azagra, Carlos Mudarra
Anal. PDE 12(4): 1065-1099 (2019). DOI: 10.2140/apde.2019.12.1065

Abstract

Let E be an arbitrary subset of n (not necessarily bounded) and f : E , G : E n be functions. We provide necessary and sufficient conditions for the 1 -jet ( f , G ) to have an extension ( F , F ) with F : n convex and C 1 . Additionally, if G is bounded we can take F so that Lip ( F ) G . As an application we also solve a similar problem about finding convex hypersurfaces of class C 1 with prescribed normals at the points of an arbitrary subset of n .

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Daniel Azagra. Carlos Mudarra. "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

Information

Received: 4 September 2017; Revised: 13 March 2018; Accepted: 30 July 2018; Published: 2019
First available in Project Euclid: 30 October 2018

zbMATH: 06991227
MathSciNet: MR3869386
Digital Object Identifier: 10.2140/apde.2019.12.1065

Subjects:
Primary: 26B05, 26B25, 52A20

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 4 • 2019
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