8 papers
Invariant metrics of model domains near pseudoconcave points
Pascal J. Thomas, Nikolai Nikolov
We give precise estimates of some holomorphically invariant infinitesimal metrics near a pseudoconcave points in a wide family of ``model'' domains for that situation in $\mathbb C…
How regular is the evolute of a plane curve?
Pascal J. Thomas, Nikolai Nikolov
We study the relationship between the smoothness of a plane curve and that of its evolute, especially in the cases where the parent curve is no more two or three times continuously…
Optimal bounds for the Kobayashi distance near -smooth boundary points
Nikolai Nikolov, Pascal J. Thomas
It is shown that the optimal upper and lower bounds for the Kobayashi distance near -smooth strongly pseudoconvex boundary points obtained in L. Kosinski, N. Niko…
Removable sets for pseudoconvexity for weakly smooth boundaries
Quang Dieu Nguyen, Pascal J. Thomas
We show that for bounded domains in with smooth boundary, if there is a closed set of -Lebesgue measure such that $\partial Ω\setminu…
Quasi Triangle Inequality for the Lempert function
Nikolai Nikolov, Pascal J. Thomas
The (unbounded version of the) Lempert function on a domain does not usually satisfy the triangle inequality, but on bounded -smooth strictly…
Boundary regularity for the distance functions, and the eikonal equation
Nikolai Nikolov, Pascal J. Thomas
We study the gain in regularity of the distance to the boundary of a domain in . In particular, we show that if the signed distance function happens to be merely diffe…
Visible -smooth domains are pseudoconvex
Nikolai Nikolov, Ahmed Yekta Ökten, Pascal J. Thomas
We show that a domain that satisfies the visibility property with -smooth boundary is pseudoconvex.
Lipschitzness of the width and diameter functions of convex bodies in
Oleg Mushkarov, Nikolai Nikolov, Pascal J. Thomas
Lipschitz constants for the width and diameter functions of a convex body in are found in terms of its diameter and thickness (maximum and minimum of both functions).…