Lipschitz normal embeddings in the space of matrices

Author(s)

Kerner, Dmitry ^[1] ; Pedersen, Helge Moller ^[2] ; Ruas, Maria A. S. ^[2]

Affiliation

^[1] Ben Gurion Univ Negev, Dept Math, Beer Sheva - Israel

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Av Trabalhador Sao Carlense, 400 Ctr, BR-13566590 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: MATHEMATISCHE ZEITSCHRIFT; v. 290, n. 1-2, p. 485-507, OCT 2018.
• Web of Science Citations: 2

Abstract

A semi-algebraic subset in R-n or C-n is naturally equipped with two different metrics, the inner metric and the outer center dot metric. Such a set (or its germ) is called Lipschitz normally embedded if the two metrics are bilipschitz equivalent. In this article we prove Lipschitz normal embeddedness of some algebraic subsets of the space of matrices. These include the space of rectangular/(skew-)synunetric/hermitian matrices of rank equal to a given number and their closures, and the upper triangular matrices with determinant 0. (In these cases we establish explicit bilipschitz constants.) We also make a short discussion about generalizing these results to determinantal varieties in real and complex spaces. (AU)

• FAPESP's process: 15/08026-4 - Bilipschitz geometry and surface singularities resolution
• Grantee: Helge Pedersen
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 14/00304-2 - Singularities of differentiable mappings: theory and applications
• Grantee: Maria Aparecida Soares Ruas
• Support Opportunities: Research Projects - Thematic Grants