Description

Book Synopsis
Features plane curves 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, rotation index, Jordan curve theorem, and isoperimetric inequality.

Table of Contents
  • 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
  • Bibliography
  • Index

Differential Geometry of Plane Curves

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    A Paperback / softback by Hilario Alencar, Walcy Santos, Gregorio Silva Neto

    £46.80

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    Order before 4pm today for delivery by Tue 15 Sep 2026.

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      Book details

      Publisher American Mathematical Society
      Published 30 July 2022
      ISBN-13 9781470469597
      978-1470469597
      ISBN-10 1470469596
      Also in:
      Topology

      Description

      Book Synopsis
      Features plane curves 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, rotation index, Jordan curve theorem, and isoperimetric inequality.

      Table of Contents
      • 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
      • Bibliography
      • Index

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