相关论文: Some remarks about Cauchy integrals

The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are…

This article discusses several matters related to Sobolev, Poincare, and isoperimetric inequalities in various settings.

In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.

In this article, we explore a series of elementary yet insightful results involving integrals related to Gaussian sums. Using techniques rooted in classical calculus, we derive several identities and evaluate nontrivial definite integrals…

We first prove a Cauchy's integral theorem and Cauchy type formula for certain inhomogeneous Cimmino system from quaternionic analysis perspective. The second part of the paper directs the attention towards some applications of the…

We develop integral geometry for non-compactly causal symmetric spaces. We define a complex horospherical transform and, for some cases, identify it with a Cauchy type integral.

Given any closed Kaehler manifold we define, following an idea by Eugenio Calabi, a Riemannian metric on the space of Kaehler metrics regarded as an infinite dimensional manifold. We prove several geometrical features of the resulting…

The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…

In this article we take a historical tour through the Cauchy-Riemann equations and their relationship with Cauchy's theorem on the independence with respect to the path of the integral of a holomorphic function. Because of its importance we…

This is a survey on nondiscrete euclidean buildings, with a focus on metric properties of these spaces.

In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.

The completeness properties of spaces of immersed curves equipped with reparametrization-invariant Riemannian metrics have recently been the subject of active research. This thesis studies the metric completion of spaces of immersed open…

This talk reviews recent developments in the field of analytical Feynman integral calculations. The central theme is the geometry associated to a given Feynman integral. In the simplest case this is a complex curve of genus zero (aka the…

We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182.

We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincar\'e duality and hard Lefschetz theorem), and their relations and applications to integral…

We extend the Cauchy residue theorem to a large class of domains including differential chains that represent, via canonical embedding into a space of currents, divergence free vector fields and non-Lipschitz curves. That is, while the…

Like his colleagues de Prony, Petit, and Poisson at the Ecole Polytechnique, Cauchy used infinitesimals in the Leibniz-Euler tradition both in his research and teaching. Cauchy applied infinitesimals in an 1826 work in differential geometry…

Treatises about General Topology that emphasize the notion of uniformity and uniform space find, of course, no difficulty in defining the notion of a complete uniform space and in constructing the completion of a metric space, via its…

We study certain generalized Cauchy integral formulas for gradients of solutions to second order divergence form elliptic systems, which appeared in recent work by P. Auscher and A. Ros\'en. These are constructed through functional calculus…

We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different…