Draft:Lipschitz Regularity Theorem

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.

Comment: It is very inappropriate to write a page on your own articles which has no wider context. The work seems relevant as it has 50 or so citations. However, it should either be merged into an existing "Lipschmit" page (there are several) or rewritten with a broader focus. Ldm1954 (talk) 12:27, 14 March 2024 (UTC)

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 $\mathbb {C} ^{n}$ that is Lipschitz regular at p must be smooth at p. In other words, if X is a complex analytic set in $\mathbb {C} ^{n}$ such that there exist open U of $\mathbb {C} ^{n}$ that contains p and a bi-Lipschitz homeomorphism h: X $\cap$ U $\to$ B, then X is smooth at p, where B is an open ball of some Euclidean space.^[1]

References[edit]

^ Sampaio, Jose Edson (2016). "Bi-Lipschitz homeomorphic subanalytic sets have bi-Lipschitz homeomorphic tangent cones". Selecta Mathematica, New Series. 22 (2): 553–559. arXiv:1412.3049. doi:10.1007/s00029-015-0195-9. S2CID 253588298.

[1] Sampaio, Jose Edson (2016). "Bi-Lipschitz homeomorphic subanalytic sets have bi-Lipschitz homeomorphic tangent cones". Selecta Mathematica, New Series. 22 (2): 553–559. arXiv:1412.3049. doi:10.1007/s00029-015-0195-9. S2CID 253588298.

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