Bilipschitz extensions from smooth manifolds.
We prove that every compact C1-submanifold of Rn, with or without boundary, has the bilipschitz extension property in Rn.
We prove that every compact C1-submanifold of Rn, with or without boundary, has the bilipschitz extension property in Rn.
We study the idea of the boundary subordination of two analytic functions. Some basic properties of the boundary subordination are discussed. Applications to classes of univalent functions referring to a boundary point are demonstrated.
We describe compact subsets K of ∂𝔻 and ℝ admitting holomorphic functions f with the domains of existence equal to ℂ∖K and such that the pluripolar hulls of their graphs are infinitely sheeted. The paper is motivated by a recent paper of Poletsky and Wiegerinck.
It is known that if is holomorphic in the open unit disc of the complex plane and if, for some , , , then . We consider a meromorphic analogue of this result. Furthermore, we introduce and study the class of meromorphic Bloch-type functions that possess a nonzero simple pole in . In particular, we obtain bounds for the modulus of the Taylor coefficients of functions in this class.