We prove that every singular algebraic curve in ℝⁿ admits local tangential Markov inequalities at each of its points. More precisely, we show that the Markov exponent at a point of a real algebraic curve A is less than or equal to twice the multiplicity of the smallest complex algebraic curve containing A.
This paper is devoted to internal capacity characteristics of a domain D ⊂ ℂⁿ, relative to a point a ∈ D, which have their origin in the notion of the conformal radius of a simply connected plane domain relative to a point. Our main goal is to study the internal Chebyshev constants and transfinite diameters for a domain D ⊂ ℂⁿ and its boundary ∂D relative to a point a ∈ D in the spirit of the author's article [Math. USSR-Sb. 25 (1975), 350-364], where similar characteristics have been investigated...
Let be a compact subset of an hyperconvex open set , forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to is a continuous...
The purpose of this paper is to present a concise survey of the main properties of biholomorphically invariant pluricomplex Green functions and to describe a number of new examples of such functions. A concept of pluricomplex geodesics is also discussed.