Related papers: Squeezing Function on Infinitely Connected Planar …
Functions that are holomorphic and Lipschitz in a smoothly bounded domain enjoy a gain in the order of Lipschitz regularity in the complex tangential directions near the boundary. We describe this gain explicitly in terms of the defining…
A nonlinear inverse problem of antiplane elasticity for a multiply connected domain is examined. It is required to determine the profile of $n$ uniformly stressed inclusions when the surrounding infinite body is subjected to antiplane…
Let $\Omega$ be a domain in $\mathbb C^n$. Suppose that $\partial\Omega$ is smooth pseudoconvex of D'Angelo finite type near a boundary point $\xi_0\in \partial\Omega$ and the Levi form has corank at most $1$ at $\xi_0$. Our goal is to show…
Let $\Omega$ be the multiply connected domain in the extended complex plane $\overline{\C}$ obtained by removing $m$ non-overlapping rectilinear segments from the infinite strip $S=\{z\,:\, \left|\Im z\right|<\pi/2\}$. In this paper, we…
This note investigates the relation between squeezing function and its generalizations. Using the relation obtained, we present an alternate method to find expression of generalized squeezing function of unit ball corresponding to the…
Comparison and localization results for the Lempert function, the Carath\'eodory distance and their infinitesimal forms on strongly pseudoconvex domains are obtained. Related results for visible and strongly complete domains are proved.
The squeezing problem on $\mathbb{C}$ can be stated as follows. Suppose that $\Omega$ is a multiply connected domain in the unit disk $\mathbb{D}$ containing the origin $z=0$. How far can the boundary of $\Omega$ be pushed from the origin…
In this paper we establish a gap theorem for the complex geometry of smoothly bounded convex domains which informally says that if the complex geometry near the boundary is close to the complex geometry of the unit ball, then the domain…
A new characterization of convexity of a planar domain is obtained. Its derivation involves two classical facts: the Varadhan's formula, expressing the distance function with respect to the domain's boundary via real-valued solutions of the…
In this paper we consider the incompressible Euler equation in a simply-connected bounded planar domain. We study the confinement of the vorticity around a stationary point vortex. We show that the power law confinement around the center of…
In this note, we give an example of a domain whose $d$-balanced squeezing function is non-plurisubharmonic.
Given a sequence of regular planar domains converging in the sense of kernel, we prove that the corresponding Green's functions converge uniformly on the complex sphere, provided the limit domain is also regular, and the connectivity is…
Using an annular version of the F. and M. Riesz theorem, we prove a generalization of the Rudin-Carleson theorem for finitely connected bounded domains. That is, for a continuous function on a closed set in the boundary of measure zero…
We propose a construction of generalized cuts of Feynman integrals as an operation on the domain of the Feynman parametric integral. A set of on-shell conditions removes the corresponding boundary components of the integration domain, in…
This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical…
We show that domains, that allow for convex functions with unbounded gradient at their boundary, are convex.
For arbitrary planar convex domain, we compute the behavior of Christoffel function up to a constant factor using comparison with other simple reference domains. The lower bound is obtained by constructing an appropriate ellipse contained…
Given an entire transcendental function f with a non-completely invariant Baker domain, we define a Baker lamination on geodesics to study the divergence and convergence of a pinching process of curves in U. If the boundary of some curve in…
We construct "large" Cantor sets whose complements resemble the unit disk arbitrarily well from the point of view of the squeezing function, and we construct "large" Cantor sets whose complements do not resemble the unit disk from the point…
The paper is centered around a new proof of the infinitesimal rigidity of convex polyhedra. The proof is based on studying derivatives of the discrete Hilbert-Einstein functional on the space of "warped polyhedra" with a fixed metric on the…