Zobrazeno 1 - 10
of 403
pro vyhledávání: '"Nikolov, Nikolai"'
Autor:
Nikolov, Nikolai, Thomas, Pascal J.
We study the gain in regularity of the distance to the boundary of a domain in $\R^m$. In particular, we show that if the signed distance function happens to be merely differentiable in a neighborhood of a boundary point, it and the boundary have to
Externí odkaz:
http://arxiv.org/abs/2409.01774
Publikováno v:
Bull. Sci. Math. 197 (2024), 103525
We show that a domain that satisfies the visibility property with $\mathcal C^2$-smooth boundary is pseudoconvex.
Comment: 6 pages; some typos and inaccuracies have been fixed. To appear in Bull. Sci. Math
Comment: 6 pages; some typos and inaccuracies have been fixed. To appear in Bull. Sci. Math
Externí odkaz:
http://arxiv.org/abs/2407.02952
Lipschitz constants for the width and diameter functions of a convex body in $\mathbb R^n$ are found in terms of its diameter and thickness (maximum and minimum of both functions). Also, a dual approach to thickness is proposed.
Externí odkaz:
http://arxiv.org/abs/2406.12537
Autor:
Bharali, Gautam, Nikolov, Nikolai
Publikováno v:
Int. J. Math. 35 (2024), no. 8, 2450031
We prove two separate lower bounds -- one for nondegenerate convex domains and the other for nondegenerate $\mathbb{C}$-convex (but not necessarily convex) domains -- for the squeezing function that hold true for all domains in $\mathbb{C}^n$, for a
Externí odkaz:
http://arxiv.org/abs/2310.08385
Studying the behavior of real and complex geodesics we provide sharp estimates for the Kobayashi distance, the Lempert function, and the Carath\'eodory distance on $\mathcal{C}^{2,\alpha}$-smooth strongly pseudoconvex domains. Similar estimates are a
Externí odkaz:
http://arxiv.org/abs/2308.09143
Autor:
Nikolov, Nikolai, Savov, Mladen
Publikováno v:
Mathematics and Informatics 67 (2024), 111-118
In this work we review and derive some elementary properties of the discrete renewal sequences based on a positive, finite and integer-valued random variable. Our results consider these sequences as dependent on the probability masses of the underlyi
Externí odkaz:
http://arxiv.org/abs/2307.00545
Autor:
Mushkarov, Oleg, Nikolov, Nikolai
We study the relationship between the areas of the consecutive quadrilaterals cut from a convex quadrilateral in the plane by means of a finite or infinite number of straight lines intersecting two of its opposite sides. Moreover, we obtain a geometr
Externí odkaz:
http://arxiv.org/abs/2305.13070
We prove that in a strongly pseudoconvex domain with smooth boundary, then the length of a geodesic for the Kobayashi-Royden infinitesimal metric between two points is bounded by a constant multiple of the Euclidean distance between the points.
Externí odkaz:
http://arxiv.org/abs/2303.04071
Autor:
Gerdjikov, Stefan, Nikolov, Nikolai
The main result of this paper is that for any norm on a complex or real $n$-dimensional linear space, every extremal basis satisfies inverted triangle inequality with scaling factor $2^n-1$. Furthermore, the constant $2^n-1$ is tight. We also prove t
Externí odkaz:
http://arxiv.org/abs/2303.03210
Autor:
Nikolov, Nikolai, Ökten, Ahmed Yekta
Publikováno v:
Proc. Amer. Math. Soc. 152 (2024), 2439-2448
Recently, the visibility property of Kobayashi (almost) geodesics has been used to provide localizations of the Kobayashi distance. In this note, we provide sufficient growth conditions for the Kobayashi distance to obtain new strong multiplicative a
Externí odkaz:
http://arxiv.org/abs/2211.15488