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Geometric Potential Analysis

Geometric Potential Analysis
Author: Mario Milman
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 370
Release: 2022-06-21
Genre: Science
ISBN: 3110741717

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This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.


Geometric Potential Analysis

Geometric Potential Analysis
Author: Mario Milman
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 272
Release: 2022-06-21
Genre: Science
ISBN: 311074189X

Download Geometric Potential Analysis Book in PDF, ePub and Kindle

This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.


Vanishing and Finiteness Results in Geometric Analysis

Vanishing and Finiteness Results in Geometric Analysis
Author: Stefano Pigola
Publisher: Springer Science & Business Media
Total Pages: 294
Release: 2008-05-28
Genre: Mathematics
ISBN: 3764386428

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This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory.


Geometric Harmonic Analysis V

Geometric Harmonic Analysis V
Author: Dorina Mitrea
Publisher: Springer Nature
Total Pages: 1006
Release: 2023-08-22
Genre: Mathematics
ISBN: 3031315618

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This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. The ultimate goal in Volume V is to prove well-posedness and Fredholm solvability results concerning boundary value problems for elliptic second-order homogeneous constant (complex) coefficient systems, and domains of a rather general geometric nature. The formulation of the boundary value problems treated here is optimal from a multitude of points of view, having to do with geometry, functional analysis (through the consideration of a large variety of scales of function spaces), topology, and partial differential equations.


Vanishing and Finiteness Results in Geometric Analysis

Vanishing and Finiteness Results in Geometric Analysis
Author: Stefano Pigola
Publisher: Birkhäuser
Total Pages: 282
Release: 2009-08-29
Genre: Mathematics
ISBN: 9783764392413

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This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory.


Geometric Harmonic Analysis IV

Geometric Harmonic Analysis IV
Author: Dorina Mitrea
Publisher: Springer Nature
Total Pages: 1004
Release: 2023-07-09
Genre: Mathematics
ISBN: 3031291794

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This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Traditionally, the label “Calderón-Zygmund theory” has been applied to a distinguished body of works primarily pertaining to the mapping properties of singular integral operators on Lebesgue spaces, in various geometric settings. Volume IV amounts to a versatile Calderón-Zygmund theory for singular integral operators of layer potential type in open sets with uniformly rectifiable boundaries, considered on a diverse range of function spaces. Novel applications to complex analysis in several variables are also explored here.


The Ethics of Technology

The Ethics of Technology
Author: Martin Peterson
Publisher: Oxford University Press
Total Pages: 265
Release: 2017-06-01
Genre: Philosophy
ISBN: 0190652276

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Autonomous cars, drones, and electronic surveillance systems are examples of technologies that raise serious ethical issues. In this analytic investigation, Martin Peterson articulates and defends five moral principles for addressing ethical issues related to new and existing technologies: the cost-benefit principle, the precautionary principle, the sustainability principle, the autonomy principle, and the fairness principle. It is primarily the method developed by Peterson for articulating and analyzing the five principles that is novel. He argues that geometric concepts such as points, lines, and planes can be put to work for clarifying the structure and scope of these and other moral principles. This geometric account is based on the Aristotelian dictum that like cases should be treated alike, meaning that the degree of similarity between different cases can be represented as a distance in moral space. The more similar a pair of cases are from a moral point of view, the closer is their location in moral space. A case that lies closer in moral space to a paradigm case for some principle p than to any paradigm for any other principle should be analyzed by applying principle p. The book also presents empirical results from a series of experimental studies in which experts (philosophers) and laypeople (engineering students) have been asked to apply the geometric method to fifteen real-world cases. The empirical findings indicate that experts and laypeople do in fact apply geometrically construed moral principles in roughly, but not exactly, the manner advocates of the geometric method believe they ought to be applied.


Geometric Function Theory

Geometric Function Theory
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
Total Pages: 311
Release: 2007-09-19
Genre: Mathematics
ISBN: 0817644407

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* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations


Conformal and Potential Analysis in Hele-Shaw Cells

Conformal and Potential Analysis in Hele-Shaw Cells
Author: Björn Gustafsson
Publisher:
Total Pages: 231
Release: 2006
Genre: Technology & Engineering
ISBN: 9780817677039

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Aims at giving a presentation of ideas that arise from the problems of planar fluid dynamics and which are interesting from the point of view of geometric function theory and potential theory. This book is concerned with geometric problems for Hele-Shaw flows.


Gaussian Capacity Analysis

Gaussian Capacity Analysis
Author: Liguang Liu
Publisher: Springer
Total Pages: 108
Release: 2018-09-20
Genre: Mathematics
ISBN: 3319950401

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This monograph develops the Gaussian functional capacity theory with applications to restricting the Gaussian Campanato/Sobolev/BV space. Included in the text is a new geometric characterization of the Gaussian 1-capacity and the Gaussian Poincaré 1-inequality. Applications to function spaces and geometric measures are also presented. This book will be of use to researchers who specialize in potential theory, elliptic differential equations, functional analysis, probability, and geometric measure theory.