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19 papers · 1 filter
A sharp Schwarz inequality on the boundary
Robert Osserman
A number of classical results reflect the fact that if a holomorphic function maps the unit disk into itself taking the origin into the origin, and if some boundary point maps…
Weak type estimates and Cotlar inequalities for Calderón-Zygmund operators in nonhomogeneous spaces
Fedor Nazarov, Sergei Treil, Alexander Volberg
In the paper we consider Calderón-Zygmund operators in nonhomogeneous spaces. We are going to prove the analogs of classical results for homogeneous spaces. Namely, we prove that a…
Singular normal form for the Painlevé equation P1
Ovidiu Costin, Rodica Daniela Costin
We show that there exists a rational change of coordinates of Painlevé's P1 equation and of the elliptic equation after which these two equations become ana…
Embedded minimal ends asymptotic to the helicoid
John McCuan, David Hoffman
The ends of a complete embedded minimal surface of {\em finite total curvature} are well understood (every such end is asymptotic to a catenoid or to a plane). We give a similar ch…
Correlation between pole location and asymptotic behavior for Painlevé I solutions
Ovidiu Costin
We extend the technique of asymptotic series matching to exponential asymptotics expansions (transseries) and show that the extension provides a method of finding singularities of…
Vertex theorems for capillary drops on support planes
Robert Finn, John McCuan
We consider a capillary drop that contacts several planar bounding walls so as to produce singularities (vertices) in the boundary of its free surface. It is shown under various co…