Geometric Analysis of PDE and Several Complex Variables: Dedicated to Franethcois Treves(Contemporary Mathematics)

This volume is dedicated to Francois Treves, who made substantial contributions to the geometric side of the theory of partial differential equations (PDEs) and several complex variables. One of his best-known contributions, reflected in many of the articles here, is the study of hypo-analytic structures. An international group of well-known mathematicians contributed to the volume. Articles of this title generally reflect the interaction of geometry and analysis that is typical of Treves' work, such as the study of the special types of partial differential equations that arise in conjunction with CR-manifolds, symplectic geometry, or special families of vector fields. There are many topics in analysis and PDEs covered here, unified by their connections to geometry. The material is suitable for graduate students and research mathematicians interested in geometric analysis of PDEs and several complex variables.

Table of Contents:
Cusp-type singularities of real analytic curves in the complex plane by P. Ahern and X. Gong The F. and M. Riesz property for vector fields by S. Berhanu and J. Hounie Gevrey hypo-ellipticity for sums of squares of vector fields: Some examples by A. Bove $W^{1,1}$-maps with values into $S^1$ by H. Brezis, P. Mironescu, and A. C. Ponce Analytic hypoellipticity and spectral problems for Schrodinger's equation by S. Chanillo Formal solutions for higher order nonlinear totally characteristic PDEs with irregular singularities by H. Chen and Z. Luo Uniqueness of $L^\infty$ solutions for a class of conormal $BV$ vector fields by F. Colombini and N. Lerner Impact of lower order terms on a model pde in two variables by P. D. Cordaro and N. Hanges Global analytic hypoellipticity for a class of quasilinear sums of squares of vector fields by M. Derridj and D. S. Tartakoff Representations via overdetermined systems by M. Eastwood A semi-explicit fundamental domain for a Picard modular group in complex hyperbolic space by G. Francsics and P. D. Lax Complex horospherical transform on real sphere by S. Gindikin On analyticity in space variable of solutions to the KdV equation by J. Gorsky and A. A. Himonas The multinomial distribution and some Bergman kernels by L. Hormander Several results for holomorphic mappings from $B^n$ into $B^N$ by X. Huang, S. Ji, and D. Xu Whitney and Mizohata structures by H. Jacobowitz One-side Liouville theorems for a class of hypoelliptic ultraparabolic equations by A. E. Kogoj and E. Lanconelli Acyclic sheaves in Banach spaces by L. Lempert A Liouville type theorem for some conformally invariant fully nonlinear equations by A. Li and Y. Y. Li Norm closure of classical pseudodifferential operators does not contain Hormander's class by S. T. Melo Remarks on the well-posedness of the nonlinear Cauchy problem by G. Metivier Representation of solutions of planar elliptic vector fields with degeneracies by A. Meziani Some recollections of working with Francois Treves by L. Nirenberg Boundary value problems on Lipschitz domains in $\mathbb{R}^n$ or $\mathbb{C}^n$ by M.-C. Shaw Hyperbolic systems well posed in all Gevrey classes by S. Spagnolo.