Non-Hyperelliptic Weierstrass Points of Maximal Weight.
Non-landing hairs in Sierpiński curve Julia sets of transcendental entire maps
We consider the family of transcendental entire maps given by where a is a complex parameter. Every map has a superattracting fixed point at z = -a and an asymptotic value at z = 0. For a > 1 the Julia set of is known to be homeomorphic to the Sierpiński universal curve, thus containing embedded copies of any one-dimensional plane continuum. In this paper we study subcontinua of the Julia set that can be defined in a combinatorial manner. In particular, we show the existence of non-landing...
Nonlinear differential monomials sharing two values
Using the notion of weighted sharing of values which was introduced by Lahiri (2001), we deal with the uniqueness problem for meromorphic functions when two certain types of nonlinear differential monomials namely
Nonlinear differential polynomials sharing a non-zero polynomial with finite weight
In the paper, dealing with a question of Lahiri (1999), we study the uniqueness of meromorphic functions in the case when two certain types of nonlinear differential polynomials, which are the derivatives of some typical linear expression, namely (), share a non-zero polynomial with finite weight. The results obtained in the paper improve, extend, supplement and generalize some recent results due to Sahoo (2013), Li and Gao (2010). In particular, we have shown that under a suitable choice of...
Nonlinear differential polynomials sharing a small function
Nonlinear differential polynomials sharing a small function
Dealing with a question of Lahiri [6] we study the uniqueness problem of meromorphic functions concerning two nonlinear differential polynomials sharing a small function. Our results will not only improve and supplement the results of Lin-Yi [16], Lahiri Sarkar [12] but also improve and supplement a very recent result of the first author [1].
Nonlinear potential theory for Sobolev spaces on Carnot groups.
Nonlinear Riemann Boundary Value Problems for a Nonlinear Elliptic System in the Plane.
Nonlinear singular integral equations involving the Hilbert transform in Clifford analysis.
Nonlinear transmission problems.
Non-maximal cyclic group actions on compact Riemann surfaces.
We say that a finite group G of automorphisms of a Riemann surface X is non-maximal in genus g if (i) G acts as a group of automorphisms of some compact Riemann surface Xg of genus g and (ii), for all such surfaces Xg , |Aut Xg| > |G|. In this paper we investigate the case where G is a cyclic group Cn of order n. If Cn acts on only finitely many surfaces of genus g, then we completely solve the problem of finding all such pairs (n,g).
Non-perturbative asymptotic improvement of perturbation theory and Mellin-Barnes representation.
Non-rectifiable limit sets of dimension one.
We construct quasiconformal deformations of convergence type Fuchsian groups such that the resulting limit set is a Jordan curve of Hausdorff dimension 1, but having tangents almost nowhere. It is known that no divergence type group has such a deformation. The main tools in this construction are (1) a characterization of tangent points in terms of Peter Jones' beta's, (2) a result of Stephen Semmes that gives a Carleson type condition on a Beltrami coefficient which implies rectifiability and (3)...
Non-recurrent meromorphic functions
We consider a transcendental meromorphic function f belonging to the class ℬ (with bounded set of singular values). We show that if the Julia set J(f) is the whole complex plane ℂ, and the closure of the postcritical set P(f) is contained in B(0,R) ∪ {∞} and is disjoint from the set Crit(f) of critical points, then every compact and forward invariant set is hyperbolic, provided that it is disjoint from Crit(f). It is further shown, under general additional hypotheses, that f admits no measurable...
Nonremovable Cantor sets for bounded quasiregular mappings.
Nontrivial expansions of zero and representation of analytic functions by series of simple fractions.
Non-uniqueness of geodesics in infinite-dimensional Teichmüller spaces. II.
Nonvanishing Univalent Functions.
Norm dependence of the coefficient map on the window size.
Norm Equalities of Analytic Mappings into Hilbert Spaces.