By Henri Skoda (auth.), P. Dolbeault, A. Iordan, G. Henkin, H. Skoda, J.-M. Trépreau (eds.)
This selection of 18 learn papers, devoted to Pierre Lelong, describes the cutting-edge on consultant difficulties of complicated research and geometry. The publication opens with an exposition of the achievements of Pierre Lelong on plurisubharmonic capabilities, closed optimistic currents, and their additional research via different mathematicians. additionally, a listing of 11 open difficulties is given. All different contributions comprise new effects similar, for instance, to the subsequent goods: - Capacities, made of optimistic currents, L2 extension theorems, Bergman kernels and metrics, new homes of convex domain names of finite variety - Non-compact limitations of Levi-flat hypersurfaces of C2, compact boundary difficulties as software of compactly supported measures orthogonal to polynomials, Hartogs' theorem on a few open subsets of a projective manifold, Malgrange vanishing theorem with aid stipulations - Embeddings for three-d CR-manifolds, geometrization of hypoellipticity, desk bound advanced curves and whole integrability - normal polynomial mappings of Ck in complicated dynamics, a right away facts of the density of repulsive cycles within the Julia set. The e-book is aimed toward researchers and complex graduate scholars in advanced and genuine research, algebraic geometry and quantity conception.