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On Lipschitz rigidity of complex analytic sets (1705.03085v3)
Published 8 May 2017 in math.AG and math.CV
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.