Local Theory -- Complex Manifolds -- Kähler Manifolds -- Vector Bundles -- Applications of Cohomology -- Deformations of Complex Structures.Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry. Recent developments in string theory have made it an highly attractive area, bot…
Differential Calculus in the Complex Plane ? -- Integral Calculus in the Complex Plane ? -- Sequences and Series of Analytic Functions, the Residue Theorem -- Construction of Analytic Functions -- Elliptic Functions -- Elliptic Modular Forms -- Analytic Number Theory -- Solutions to the Exercises.The guiding principle of this presentation of ``Classical Complex Analysis'' is to proceed as quick…
This volume is an expanded version of Chapters III, IV, V and VII of my 1963 book "Linear partial differential operators". In addition there is an entirely new chapter on convolution equations, one on scattering theory, and one on methods from the theory of analytic functions of several complex variables. The latter is somewhat limited in scope though since it seems superfluous to duplicate the…
Holomorphic Functions -- Complex Manifolds -- Differential Forms, Vector Bundles, Sheaves -- Infinitesimal Deformation -- Theorem of Existence -- Theorem of Completeness -- Theorem of Stability.From the reviews: "The author, who with Spencer created the theory of deformations of a complex manifold, has written a book which will be of service to all who are interested in this by now vast subject…