Log-Lipschitz and H\"older regularity imply smoothness for complex
analytic sets
Log-Lipschitz and H\"older regularity imply smoothness for complex
analytic sets
In this paper, we prove metric analogues, in any dimension and in any co-dimension, of the famous Theorem of Mumford on smoothness of normal surfaces and the beautiful Theorem of Ramanujam that gives a topological characterization of $\mathbb{C}^2$ as an algebraic surface. For instance, we prove that a complex analytic …