7 citations · 7 across the 6 of their papers we have counts for
8 papers
Local quasi-isometries and tangent cones of definable germs
Nhan Nguyen
In this paper, we introduce the notion of local quasi-isometry for metric germs and prove that two definable germs are quasi-isometric if and only if their tangent cones are bi-Lip…
On a link criterion for Lipschitz normal embeddings among definable sets
Nhan Nguyen
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 thi…
Bi-Lipschitz contact invariance of rank
Nhan Nguyen
In this note we show that the rank of a smooth map is a bi-Lipschitz contact invariant. As a consequence, the first Boardman symbol and its length are bi-Lipschitz contact invarian…
Classification of Lipschitz simple function germs
Nhan Nguyen, Maria Ruas, Saurabh Trivedi
It is known that the bi-Lipschitz right classification of function germs admit moduli. In this article we introduce a notion called the Lipschitz simple function germs and present…
Transversality of smooth definable maps in O-minimal structures
Nhan Nguyen, Saurabh Trivedi
We present a definable smooth version of the Thom transversality theorem. We show further that the set of non-transverse definable smooth maps is nowhere dense in the definable smo…
Tangent cones and regularity of definable sets
Krzysztof Kurdyka, Olivier Le Gal, Nhan Nguyen
Let be a connected locally closed definable set in an o-minimal structure. We prove that the following three statements are equivalent: (i) is a ma…
Whitney stratifications and the continuity of local Lipschitz Killing curvatures
Nhan Nguyen, Guillaume Valette
We prove that local Lipschitz Killing curvatures of definable sets in a polynomially bounded o-minimal structure are continuous along strata of Whitney stratifications and locally…
A geometric proof of the existence of definable Whitney stratifications
Nhan Nguyen, Saurabh Trivedi, David Trotman
We give a geometric proof of existence of Whitney stratifications of definable sets in o-minimal structures.