The special case of a holomorphic function, defined in a punctured disc is the topic of the remainder of the chapter. The center of the disc is in that case said to be an isolated singularity of the function. We classify isolated singularities into removable singularities, poles and essential...
In complex analysis, a branch of mathematics, an isolated singularity is one that has no other singularities close to it. In other words, a complex number z is an isolated singularity of a function f if there exists an open disk D centered at z such that f is holomorphic on D {z}, ...
Many important tools of complex analysis such as Laurent series and the residue theorem require that all relevant singularities of the function be isolated. 复分析中许多有用的工具,例如洛朗展开、留数定理等,都需要保证相关奇点的孤立性才能应用。 WikiMatrix In particular he has made substantial contr...
A Serrin-like condition is found for removability of the isolated singularity for high-order elliptic equations in divergent form whose coefficients satisfy a polynomial growth conditions and an ellipticity condition stronger than one that usually is considered for high-order elliptic equations.关键词:...
We represent the complex gradient ∂z u around a non–removable polar singularity z 0 in terms of a series expansion of a quasiconformal mapping H, where m being the index of D u in z 0:. The analysis of the asymptotic behavior of H gives power estimates from above and below for |...
The condition of solvability of the initial nonlinear integrodifferential equation describing the shape of the crystallization front is reduced, in the weak anisotropy limit, to the condition that the solution of the linear differential equation is finite near a singularity in a complex plane. The ...
The asymptotic behavior of conformal metrics with negative curvatures near an isolated singularity for at most second order derivatives was described by Kraus and Roth in one of their papers in 2008. Our work improves one estimate of theirs and shows the estimate for higher order derivatives near ...
In this paper we prove the following conjecture of Brieskorn: "The complex of (holomorphic) differential forms of an isolated hypersurface singularity of dimension n>1 is exact in degree n1." M Sebastiani - 《Manuscripta Mathematica》 被引量: 109发表: 1970年 Preuve d'une conjecture de Briesko...
[ m a t h . A G ] 1 1 S e p 2 0 0 2 ContinuousInvariantsofIsolated HypersurfaceSingularities MichaelG.Eastwood PureMathematicsDepartment,AdelaideUniversity,SouthAustralia5005 E-mail:meastwoo@maths.adelaide.edu.au 1Introduction SupposeVisacomplexhypersurfaceinC n withanisolatedsingularityatthe origin...
Singularity theory stands at a cross-road of mathematics, a meeting point where manyareasofmathematicscometogether,suchasgeometry,topologyandalgebra, analysis,di?erential equations and dynamical systems, combinatoricsand number theory, to mention some of them. Thus, one who would write a book about ...