A path-connected subanalytic subset in is naturally equipped with two metrics: the inner and
the outer metrics. We say that a subset is Lipschitz normally embedded (LNE) if these two …

We study Lipschitz geometry of fibers of complex polynomial mappings from two points of
view: the equivalence of inner and outer metrics of an algebraic curve and the existence of a …

Abstract Any subanalytic germ (X, 0)⊂(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 …

We compare ambient and outer Lipschitz geometry of Lipschitz normally embedded H\"
older triangles in $\mathbb {R}^ 4$. In contrast to the case of $\mathbb {R}^ 3$ there are …

A normal pair of H\" older triangles is the union of two normally embedded H\" older triangles
satisfying some natural conditions on the tangency orders of their boundary arcs. It is a …

We study outer Lipschitz geometry of real semialgebraic or, more general, definable in a
polynomially bounded o-minimal structure over the reals, surface germs. In particular, any …

Any germ of a complex analytic space is equipped with two natural metrics: the outer metric
induced by the hermitian metric of the ambient space and the inner metric, which is the …

In this article, we prove that for a definable set in an o‐minimal structure with connected link
(at 0 or infinity), the inner distance of the link is equivalent to the inner distance of the set …

It is known by a result of Mendes and Sampaio that the Lipschitz normal embedding of a
subanalytic germ is fully characterized by the Lipschitz normal embedding of its link. In this …

The paper is devoted to relations between topological and metric properties of germs of real
surfaces, obtained by analytic maps from R^ 2 R 2 to R^ 4. R 4. We show that for a big class …