Uniform domains and -domains in Carnot groups.
Uniform domains and quasiconformal mappings on the Heisenberg groups.
Uniqueness and Free Interpolation for Logarithmic Potentials and the Cauchy Problem for the Laplace Equation in R2.
Uniqueness and Stability of Harmonic Maps and Their Jacobi Fields.
Uniqueness of Dirichlet, Neumann, and mixed boundary value problems for Laplace's and Poisson's equations for a rectangle.
Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains
Uniqueness theorems for Cauchy integrals
Univalent harmonic exterior mappings as solutions of an optimization problem
Univalent harmonic mappings
Let a < 0, Ω = ℂ -(-∞, a] and U = z: |z| < 1. We consider the class of functions f which are univalent, harmonic and sense preserving with f(U) = Ω and satisfy f(0) = 0, and . We describe the closure of and determine the extreme points of .
Univalent harmonic mappings II
Let a < 0 < b and Ω(a,b) = ℂ - ((-∞, a] ∪ [b,+∞)) and U= z: |z| < 1. We consider the class of functions f which are univalent, harmonic and sense-preserving with f(U) = Ω and satisfying f(0) = 0, and .
Univalent Harmonic Mappings of Annuli
Universal harmonic functions on the hyperbolic space
We prove universal overconvergence phenomena for harmonic functions on the real hyperbolic space.
Universal Taylor series, conformal mappings and boundary behaviour
A holomorphic function on a simply connected domain is said to possess a universal Taylor series about a point in if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta outside (provided only that has connected complement). This paper shows that this property is not conformally invariant, and, in the case where is the unit disc, that such functions have extreme angular boundary behaviour.
Upper bounds and conservativeness for semigroups associated with a class of Dirichlet forms generated by pseudo differential operators.
Use of logarithmic sums to estimate polynomials.