5 papers
On Ulam's Segment Motion Problem
Dragomir Grozev, Nikolai Nikolov
We study extremal rigid motions of a unit segment in , . Given two prescribed positions of a unit segment, we consider continuous motions transforming the ini…
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…
Precise estimates of invariant distances on strongly pseudoconvex domains
Åukasz KosiÅski, Nikolai Nikolov, Ahmed Yekta Ãkten
Studying the behavior of real and complex geodesics we provide sharp estimates for the Kobayashi distance, the Lempert function, and the Carathéodory distance on $\mathcal{C}^{2,΅
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 Ãkten, Pascal J. Thomas
We show that a domain that satisfies the visibility property with -smooth boundary is pseudoconvex.