Kirszbraun Theorem

In mathematics, the Kirszbraun theorem in mathematical analysis states that if U is a subset of Euclidean space En and
f : U → Em
is a Lipschitz-continuous map, then there is a Lipschitz-continuous map
F: En → Em
that extends f, and has the same Lipschitz constant as f.

Reference

M. D. Kirszbraun. Uber die zusammenziehenden und Lipschitzchen Transformationen. Fund. Math., (22):77108, 1934.

 

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