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The Lipschitz Regularity Theorem is a result in complex algebraic geometry that characterizes the complex analytic sets that are smooth from the metric point of view. It was proved by José Edson Sampaio, a Brazilian mathematician and professor at the Universidade Federal do Ceará.
The theorem states that any complex analytic set X in that is Lipschitz regular at p must be smooth at p. In other words, if X is a complex analytic set in such that there exist open U of that contains p and a bi-Lipschitz homeomorphism h: X U B, then X is smooth at p, where B is an open ball of some Euclidean space. [1]
Submission rejected on 14 March 2024 by
Ldm1954 (
talk). This submission is contrary to the purpose of Wikipedia. Rejected by Ldm1954 2 months ago. Last edited by Ldm1954 2 months ago. |
A major contributor to this article appears to have a
close connection with its subject. (March 2024) |
The Lipschitz Regularity Theorem is a result in complex algebraic geometry that characterizes the complex analytic sets that are smooth from the metric point of view. It was proved by José Edson Sampaio, a Brazilian mathematician and professor at the Universidade Federal do Ceará.
The theorem states that any complex analytic set X in that is Lipschitz regular at p must be smooth at p. In other words, if X is a complex analytic set in such that there exist open U of that contains p and a bi-Lipschitz homeomorphism h: X U B, then X is smooth at p, where B is an open ball of some Euclidean space. [1]