Core Concepts
The article establishes conditions for the existence of continuous extensions of Lipschitz maps and monotone maps in Hilbert spaces, particularly focusing on preserving the uniform distance between the extended map and a given reference map.
Stats
The paper focuses on maps with values in R^m where m is less than or equal to 3.
The paper utilizes the fact that the infimum of distances between a point and convex combinations of other points in a set is bounded below by 1/sqrt(2) in specific cases.