Title: A short survey on Lipschitz extension problems

Abstract: 

    Let X and Y be metric spaces, S be a closed subset of X, and f be a Lipschitz map from S to Y. How can we know if f can be extended to globally defined Lipschitz map preserving (or almost preserving) the Lipschitz constant of f? How do we construct such an extension? For what kind of metric spaces can this always be done? 
    In this series, we survey some of the key results in the study of the Lipschitz extension problem. We will start by introducing classical construction by McShane and Whitney and an existence result by Kirszbraun. Tentatively, we will explore some of the more advanced flavors, including the ball intersection property (existence), Nagata dimension and connectedness (constructive), and a recent explicit Kirszbraun formula by D. Azagra et. al


•	McShane: https://www.ams.org/journals/bull/1934-40-12/S0002-9904-1934-05978-0/S0002-9904-1934-05978-0.pdf
•	Whitney: https://www.ams.org/journals/tran/1934-036-01/S0002-9947-1934-1501735-3/
•	Explicit Kirszbraun formula: https://arxiv.org/abs/1810.10288
•	Nagata dimension and extension: https://arxiv.org/abs/math/0410048
•	Roadmap book: 
o	Volume 1: https://link.springer.com/book/10.1007/978-3-0348-0209-3
o	Volume 2: https://link.springer.com/book/10.1007/978-3-0348-0212-3