Residue calculus for c-holomorphic functions

Residue Currents of Holomorphic Morphisms

Given a generically surjective holomorphic vector bundle morphism f : E → Q, E and Q Hermitian bundles, we construct a current R with values in Hom (Q,H), where H is a certain derived bundle, and with support on the set Z where f is not surjective. The main property is that if φ is a holomorphic section of Q, and Rφ = 0, then locally fψ = φ has a holomorphic solution ψ. In the generic case also...

Multicentric Holomorphic Calculus

Certain subclass of $p$-valent meromorphic Bazilevi'{c} functions defined by fractional $q$-calculus operators

The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...

Residue Calculus and Applications

We present a new algorithm in order to compute the multidimensional residue of a polynomial map based on a perturbation argument and the Generalized Transformation Law. Then we use it for studying some fundamental problems in Computer Aided Geometric Design.

From Holomorphic Functions to Holomorphic Sections

It is a pleasure to have the opportunity in the graduate colloquium to introduce my research field. I am a differential geometer. To be more precise, I am a complex differential geometer, although I am equally interested in real differential geometry. To many people, geometry is a kind of mathematics that is related to length, area, volume, etc. For the Euclidean geometry, this is indeed the ca...