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.
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.
Hilario Alencar, Federal University of Alagoas, Maceio, Alagoas, Brazil. Walcy Santos, Federal University of Rio de Janeiro, Brazil. Gregorio Silva Neto, Universidade Federal de Alagoas, Maceio, Alagoas, Brazil.
Inhaltsangabe
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
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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