Work

Global Lipschitz geometry of conic singular sub-manifolds with applications to algebraic sets

Year: 2024

Type: article

Abstract: We prove that a connected globally conic singular sub-manifold of a Riemannian manifold, compact when the ambient manifold is non-Euclidean, is Lipschitz Normally Embedded: its outer and inner metric space structures are equivalent. Moreover, we show that generic \mathbb{K} -analytic germs as well as generic affine algebraic sets in \mathbb{K}^{n} , where \mathbb{K}=\mathbb{C} or \mathbb{R} , are globally conic singular sub-manifolds. Consequently, a generic \mathbb{K} -analytic germ or a generic algebraic subset of \mathbb{K}^{n} is Lipschitz Normally Embedded.

Source: Documenta Mathematica

DOI: 10.4171/dm/975

Authors: André Costa, Vincent Grandjean, Maria Michalska

Institutions: Universidade Estadual do Ceará, Universidade Federal de Santa Catarina, University of Łódź

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Fundação de Amparo à Pesquisa do Estado de São Paulo

Awards: G295657101, G6190682352