Artin’s approximation theorems and Cauchy-Riemann geometry

The Cauchy-riemann Equations and Differential Geometry

On symmetric Cauchy-Riemann manifolds

The Riemannian symmetric spaces play an important role in different branches of mathematics. By definition, a (connected) Riemannian manifold M is called symmetric if, to every a ∈ M , there exists an involutory isometric diffeomorphism sa:M → M having a as isolated fixed point in M (or equivalently, if the differential dasa is the negative identity on the the tangent space Ta = TaM of M at a)....

Cauchy-stieltjes and Riemann-stielt Jes Integrals

Bivariant Riemann Roch Theorems

The goal of this paper is to explain the analogy between certain results in algebraic geometry, namely the Riemann-Roch theorems due to Baum,Fulton, and MacPherson ([BFM2],and [FMac]); and recent results in geometric topology due to Dwyer, Weiss and myself [DWW]. One reason for doing this is that the bivariant viewpoint introduced by Fulton-MacPherson in their memoir [FMac], becomes particularl...

Uniqueness Theorems for Cauchy Integrals

If μ is a finite complex measure in the complex plane C we denote by C its Cauchy integral defined in the sense of principal value. The measure μ is called reflectionless if it is continuous (has no atoms) and C = 0 at μ-almost every point. We show that if μ is reflectionless and its Cauchy maximal function Cμ ∗ is summable with respect to |μ| then μ is trivial. An example of a reflectionless m...