Geodesic
Global Lipschitz geometry of conic singular sub-manifolds with applications to algebraic sets
Documenta mathematica, Tome 29 (2024) no. 6, pp. 1341-1366

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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 K-analytic germs as well as generic affine algebraic sets in Kn, where K=C or R, are globally conic singular sub-manifolds. Consequently, a generic K-analytic germ or a generic algebraic subset of Kn is Lipschitz Normally Embedded.
DOI : 10.4171/dm/975
Classification : 51K99, 14P99, 53B99, 58K99
Mots-clés : conic singularity, generic algebraic set, Lipschitz geometry, quasiconvex set, Lipschitz normally embedded set 
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André Costa; Vincent Grandjean; Maria Michalska. Global Lipschitz geometry of conic singular sub-manifolds with applications to algebraic sets. Documenta mathematica, Tome 29 (2024) no. 6, pp. 1341-1366. doi: 10.4171/dm/975

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