On Lipschitz rigidity of complex analytic sets

2017/05/08 by Fernandes, Alexandre, Sampaio, J. Edson · 1 citation
#14B05 #32S50 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.03085

Abstract

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

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• Lipschitz geometry of the image of finite mappings

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