On Lipschitz rigidity of complex analytic sets

Abstract

We prove that any complex analytic set in ${\mathbb{C}}^n$ which is Lipschitz normally embedded at infinity and has tangent cone at infinity that is a linear subspace of ${\mathbb{C}}^n$ must be an affine linear subspace of ${\mathbb{C}}^n$ itself. No restrictions on the singular set, dimension nor codimension are required. In particular, a complex algebraic set in ${\mathbb{C}}^n$ which is Lipschitz regular at infinity is an affine linear subspace.

arXiv commentRevision in the statement of Corollary 5.7 and it is added Example 5.8. 12 pages