On Lipschitz Normally Embedded Singularities

Lorenzo Fantini () and Anne Pichon ()
Additional contact information
Lorenzo Fantini: Institut Polytechnique de Paris, Centre de Mathématiques Laurent Schwartz, Ecole Polytechnique and CNRS
Anne Pichon: Aix-Marseille Univ, CNRS

Chapter Chapter 10 in Handbook of Geometry and Topology of Singularities IV, 2023, pp 497-519 from Springer

Abstract: Abstract Any subanalytic germ ( X , 0 ) ⊂ ( ℝ n , 0 ) $$(X,0) \subset ( {\mathbb R}^n,0)$$ is equipped with two natural metrics: its outer metric, induced by the standard Euclidean metric of the ambient space, and its inner metric, which is defined by measuring the shortest length of paths on the germ ( X , 0 ) $$(X,0)$$ . The germs for which these two metrics are equivalent up to a bilipschitz homeomorphism, which are called Lipschitz Normally Embedded, have attracted a lot of interest in the last decade. In this survey we discuss many general facts about Lipschitz Normally Embedded singularities, before moving our focus to some recent developments on criteria, examples, and properties of Lipschitz Normally Embedded complex surfaces. We conclude the manuscript with a list of open questions which we believe to be worth of interest.

Date: 2023
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-31925-9_10

Ordering information: This item can be ordered from
http://www.springer.com/9783031319259

DOI: 10.1007/978-3-031-31925-9_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().