Sharp bounds of the third Hankel determinant for classes of univalent functions with bounded turning
We improve the bounds of the third order Hankel determinant for two classes of univalent functions with bounded turning.
Sharp endpoint results for imaginary powers and Riesz transforms on certain noncompact manifolds
We consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the imaginary powers of the Laplacian and the Riesz transform are bounded from the Hardy space X¹(M), introduced in previous work of the authors, to L¹(M).
Sharp estimates for hyperbolic metrics and covering theorems of Landau type.
Sharp Estimates For Some Integral Operators Of Convex Functions Of Order Alpha
Sharp estimates of the curvature of some free boundaries in two dimensions.
Sharp estimation of even coefficients of bounded symmetric univalent functions
Sharp estimation of the coefficients of bounded univalent functions close to identity [Book]
Sharp norm estimate of Schwarzian derivative for a class of convex functions
We establish a sharp norm estimate of the Schwarzian derivative for a function in the classes of convex functions introduced by Ma and Minda [Proceedings of the Conference on Complex Analysis, Int. Press, 1992, 157-169]. As applications, we give sharp norm estimates for strongly convex functions of order α, 0 < α < 1, and for uniformly convex functions.
Shearing hyperbolic surfaces, bending pleated surfaces and Thurston's symplectic form
Short separating geodesics for multiply connected domains
We consider the following questions: given a hyperbolic plane domain and a separation of its complement into two disjoint closed sets each of which contains at least two points, what is the shortest closed hyperbolic geodesic which separates these sets and is it a simple closed curve? We show that a shortest geodesic always exists although in general it may not be simple. However, one can also always find a shortest simple curve and we call such a geodesic a meridian of the domain. We prove that,...
Similarity of operators and geometry of eigenvector bundles.
Simple polynomials
Simple sufficient conditions for starlikeness and convexity for meromorphic functions
In this paper we investigate some extensions of sufficient conditions for meromorphic multivalent functions in the open unit disk to be meromorphic multivalent starlike and convex of order α. Our results unify and extend some starlikeness and convexity conditions for meromorphic multivalent functions obtained by Xu et al. [2], and some interesting special cases are given.
Simply connected quasiregularly elliptic 4-manifolds.
Simultaneous uniformisation.
Sine - Laplace Equation, Sinh-Laplace Equation and Harmonic Maps.
Singular behavior of conformal Martin kernels and non-tangential limits of conformal mappings.
Singular Cauchy integrals and conformal welding on Jordan curves.
Singular functions on metric measure spaces.
On relatively compact domains in metric measure spaces we construct singular functions that play the role of Green functions of the p-Laplacian. We give a characterization of metric spaces that support a global version of such singular function, in terms of capacity estimates at infinity of such metric spaces. In addition, when the measure of the space is locally Q-regular, we study quasiconformal invariance property associated with the existence of global singular functions.
Singular Integrals, Analytic Capacity and Rectifiability.