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Differential Geometry of Plane Curves
 
Hilário Alencar Federal University of Alagoas, Maceió, Alagoas, Brazil
Walcy Santos Federal University of Rio de Janeiro, Rio de Janeiro, Brazil
Gregório Silva Neto Universidade Federal de Alagoas, Maceió, Alagoas, Brazil
Front Cover for Differential Geometry of Plane Curves
Available Formats:
Softcover ISBN: 978-1-4704-6959-7
Product Code: STML/96
List Price: $59.00
Individual Price: $47.20
Electronic ISBN: 978-1-4704-7036-4
Product Code: STML/96.E
List Price: $59.00
Individual Price: $47.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $88.50
Front Cover for Differential Geometry of Plane Curves
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  • Front Cover for Differential Geometry of Plane Curves
  • Back Cover for Differential Geometry of Plane Curves
Differential Geometry of Plane Curves
Hilário Alencar Federal University of Alagoas, Maceió, Alagoas, Brazil
Walcy Santos Federal University of Rio de Janeiro, Rio de Janeiro, Brazil
Gregório Silva Neto Universidade Federal de Alagoas, Maceió, Alagoas, Brazil
Available Formats:
Softcover ISBN:  978-1-4704-6959-7
Product Code:  STML/96
List Price: $59.00
Individual Price: $47.20
Electronic ISBN:  978-1-4704-7036-4
Product Code:  STML/96.E
List Price: $59.00
Individual Price: $47.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $88.50
  • Book Details
     
     
    Student Mathematical Library
    Volume: 962022; 416 pp
    MSC: Primary 53;

    This book features plane curves—the simplest objects in differential geometry—to illustrate many deep and inspiring results in the field in an elementary and accessible way.

    After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the four-vertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curve-shortening flow that is based on original articles but requires a minimum of previous knowledge.

    Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills. Prerequisites are courses in standard one variable calculus and analytic geometry on the plane.

    Readership

    Undergraduate and graduate students interested in curves in the Euclidean plane.

  • Table of Contents
     
     
    • Chapters
    • Plane curves
    • Winding number
    • Rotation index
    • Jordan curve theorem
    • Isoperimetric inequality
    • Convex curves
    • The four-vertex theorem
    • Curve-shortening flow
    • Appendix A. The class $\mathcal {C}^\infty $ convergence of the curvature function under the curve-shortening flow
    • Appendix B. Answers to selected exercises
  • Requests
     
     
    Review Copy – for reviewers who would like to review an AMS book
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 962022; 416 pp
MSC: Primary 53;

This book features plane curves—the simplest objects in differential geometry—to illustrate many deep and inspiring results in the field in an elementary and accessible way.

After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the four-vertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curve-shortening flow that is based on original articles but requires a minimum of previous knowledge.

Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills. Prerequisites are courses in standard one variable calculus and analytic geometry on the plane.

Readership

Undergraduate and graduate students interested in curves in the Euclidean plane.

  • Chapters
  • Plane curves
  • Winding number
  • Rotation index
  • Jordan curve theorem
  • Isoperimetric inequality
  • Convex curves
  • The four-vertex theorem
  • Curve-shortening flow
  • Appendix A. The class $\mathcal {C}^\infty $ convergence of the curvature function under the curve-shortening flow
  • Appendix B. Answers to selected exercises
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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