Curvature: A Variational Approach PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Curvature: A Variational Approach PDF full book. Access full book title Curvature: A Variational Approach by A. Agrachev. Download full books in PDF and EPUB format.
Author: A. Agrachev
Publisher: American Mathematical Soc.
ISBN: 1470426463
Category : Mathematics
Languages : en
Pages : 154
Get Book Here
Book Description
The curvature discussed in this paper is a far reaching generalization of the Riemannian sectional curvature. The authors give a unified definition of curvature which applies to a wide class of geometric structures whose geodesics arise from optimal control problems, including Riemannian, sub-Riemannian, Finsler and sub-Finsler spaces. Special attention is paid to the sub-Riemannian (or Carnot–Carathéodory) metric spaces. The authors' construction of curvature is direct and naive, and similar to the original approach of Riemann. In particular, they extract geometric invariants from the asymptotics of the cost of optimal control problems. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.
Author: A. Agrachev
Publisher: American Mathematical Soc.
ISBN: 1470426463
Category : Mathematics
Languages : en
Pages : 154
Get Book Here
Book Description
The curvature discussed in this paper is a far reaching generalization of the Riemannian sectional curvature. The authors give a unified definition of curvature which applies to a wide class of geometric structures whose geodesics arise from optimal control problems, including Riemannian, sub-Riemannian, Finsler and sub-Finsler spaces. Special attention is paid to the sub-Riemannian (or Carnot–Carathéodory) metric spaces. The authors' construction of curvature is direct and naive, and similar to the original approach of Riemann. In particular, they extract geometric invariants from the asymptotics of the cost of optimal control problems. Surprisingly, it works in a very general setting and, in particular, for all sub-Riemannian spaces.
Author: Michael Struwe
Publisher: Springer Science & Business Media
ISBN: 3662041944
Category : Science
Languages : en
Pages : 292
Get Book Here
Book Description
Hilberts talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateaus problem by Douglas and Rad. This third edition gives a concise introduction to variational methods and presents an overview of areas of current research in the field, plus a survey on new developments.
Author: Frederick J. Almgren
Publisher: American Mathematical Soc.
ISBN: 9780821810675
Category : Mathematics
Languages : en
Pages : 638
Get Book Here
Book Description
This volume offers a unique collection of some of the work of Frederick J. Almgren, Jr., the man most noted for defining the shape of geometric variational problems and for his role in founding The Geometry Center. Included in the volume are the following: a summary by Sheldon Chang of the famous 1700 page paper on singular sets of area-minimizing $m$-dimensional surfaces in $Rn$, a detailed summary by Brian White of Almgren's contributions to mathematics, his own announcements of several longer papers, important shorter papers, and memorable expository papers. Almgren's enthusiasm for the subject and his ability to locate mathematically beautiful problems that were "ready to be solved" attracted many students who further expanded the subject into new areas. Many of these former students are now known for the clarity of their expositions and for the beauty of the problems that they work on. As Almgren's former graduate student, wife, and colleague, Professor Taylor has compiled an important volume on an extraordinary mathematician. This collection presents a fine comprehensive view of the man's mathematical legacy
Author: R. Tyrrell Rockafellar
Publisher: Springer Science & Business Media
ISBN: 3642024319
Category : Mathematics
Languages : en
Pages : 747
Get Book Here
Book Description
From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Author: Patrick Knupp
Publisher: CRC Press
ISBN: 0429605307
Category : Mathematics
Languages : en
Pages : 312
Get Book Here
Book Description
Fundamentals of Grid Generation is an outstanding text/reference designed to introduce students in applied mathematics, mechanical engineering, and aerospace engineering to structured grid generation. It provides excellent reference material for practitioners in industry, and it presents new concepts to researchers. Readers will learn what boundary-conforming grids are, how to generate them, and how to devise their own methods. The text is written in a clear, intuitive style that doesn't get bogged down in unnecessary abstractions. Topics covered include planar, surface, and 3-D grid generation; numerical techniques; solution adaptivity; the finite volume approach to discretization of hosted equations; concepts from elementary differential geometry; and the transformation of differential operators to general coordinate systems. The book also reviews the literature on algebraic, conformal, orthogonal, hyperbolic, parabolic, elliptic, biharmonic, and variational approaches to grid generation. This unique volume closes with the author's original methods of variational grid generation.
Author: David Bleecker
Publisher: Courier Corporation
ISBN: 0486445461
Category : Science
Languages : en
Pages : 202
Get Book Here
Book Description
This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.
Author: Max K. Agoston
Publisher: Springer Science & Business Media
ISBN: 9781852338183
Category : Computers
Languages : en
Pages : 960
Get Book Here
Book Description
Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modeling, this two-volume work covers implementation and theory in a thorough and systematic fashion. It covers the computer graphics part of the field of geometric modeling and includes all the standard computer graphics topics. The CD-ROM features two companion programs.
Author: Kartik Venkataraman
Publisher:
ISBN:
Category :
Languages : en
Pages : 468
Get Book Here
Book Description
Author: Management Association, Information Resources
Publisher: IGI Global
ISBN: 1609605624
Category : Medical
Languages : en
Pages : 2256
Get Book Here
Book Description
"This multi-volume book delves into the many applications of information technology ranging from digitizing patient records to high-performance computing, to medical imaging and diagnostic technologies, and much more"--
Author: Yuri Boykov
Publisher: Springer
ISBN: 3642230946
Category : Computers
Languages : en
Pages : 437
Get Book Here
Book Description
This book constitutes the refereed proceedings of the 8th International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2011, held in St. Petersburg, Russia in July , 2011. The book presents 30 revised full papers selected from a total of 52 submissions. The book is divided in sections on discrete and continuous optimization, segmentation, motion and video, learning and shape analysis.
