Provides an extensive introduction to a few of the most prominent extrinsic flows, namely the curve shortening flow, the mean curvature flow, the Gauss curvature flow, the inverse-mean curvature flow, and fully nonlinear flows of mean curvature and inverse-mean curvature type.
Provides an extensive introduction to a few of the most prominent extrinsic flows, namely the curve shortening flow, the mean curvature flow, the Gauss curvature flow, the inverse-mean curvature flow, and fully nonlinear flows of mean curvature and inverse-mean curvature type.
Ben Andrews, The Australian National University, Canberra, Australia. Bennett Chow, University of California, San Diego, La Jolla, CA. Christine Guenther, Pacific University, Forest Grove, OR. Mat Langford, University of Tennessee, Knoxville, TN.
Inhaltsangabe
1. The heat equation 2. Introduction to curve shortening 3. The Gage-Hamilton-Grayson theorem 4. Self-similar and ancient solutions 5. Hypersurfaces in Euclidean space 6. Introduction to mean curvature flow 7. Mean curvature flow of entire graphs 8. Huisken's theorem 9. Mean convex mean curvature flow 10. Monotonicity formulae 11. Singularity analysis 12. Noncollapsing 13. Self-similar solutions 14. Ancient solutions 15. Gauss curvature flows 16. The affine normal flow 17. Flows by superaffine powers of the Gauss curvature 18. Fully nonlinear curvature flows 19. Flows of mean curvature type 20. Flows of inverse-mean curvature type 21. Bibliography 22. Index
1. The heat equation 2. Introduction to curve shortening 3. The Gage-Hamilton-Grayson theorem 4. Self-similar and ancient solutions 5. Hypersurfaces in Euclidean space 6. Introduction to mean curvature flow 7. Mean curvature flow of entire graphs 8. Huisken's theorem 9. Mean convex mean curvature flow 10. Monotonicity formulae 11. Singularity analysis 12. Noncollapsing 13. Self-similar solutions 14. Ancient solutions 15. Gauss curvature flows 16. The affine normal flow 17. Flows by superaffine powers of the Gauss curvature 18. Fully nonlinear curvature flows 19. Flows of mean curvature type 20. Flows of inverse-mean curvature type 21. Bibliography 22. Index
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