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.

• The heat equationIntroduction to curve shorteningThe Gage-Hamilton-Grayson theoremSelf-similar and ancient solutionsHypersurfaces in Euclidean spaceIntroduction to mean curvature flowMean curvature flow of entire graphsHuisken's theoremMean convex mean curvature flowMonotonicity formulaeSingularity analysisNoncollapsingSelf-similar solutionsAncient solutionsGauss curvature flowsThe affine normal flowFlows by superaffine powers of the Gauss curvatureFully nonlinear curvature flowsFlows of mean curvature typeFlows of inverse-mean curvature typeBibliographyIndex

This textbook, written by four experts in the field, offers an authoritative introduction and overview to the topic of extrinsic geometric flows. It will serve well as a primary text for a graduate student who already has background knowledge of differential geometry and (some) partial differential equations. It will also serve as a useful reference for experts in the field."" - John Ross, Southwestern University

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.

• The heat equationIntroduction to curve shorteningThe Gage-Hamilton-Grayson theoremSelf-similar and ancient solutionsHypersurfaces in Euclidean spaceIntroduction to mean curvature flowMean curvature flow of entire graphsHuisken's theoremMean convex mean curvature flowMonotonicity formulaeSingularity analysisNoncollapsingSelf-similar solutionsAncient solutionsGauss curvature flowsThe affine normal flowFlows by superaffine powers of the Gauss curvatureFully nonlinear curvature flowsFlows of mean curvature typeFlows of inverse-mean curvature typeBibliographyIndex

This textbook, written by four experts in the field, offers an authoritative introduction and overview to the topic of extrinsic geometric flows. It will serve well as a primary text for a graduate student who already has background knowledge of differential geometry and (some) partial differential equations. It will also serve as a useful reference for experts in the field."" - John Ross, Southwestern University

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.

• The heat equationIntroduction to curve shorteningThe Gage-Hamilton-Grayson theoremSelf-similar and ancient solutionsHypersurfaces in Euclidean spaceIntroduction to mean curvature flowMean curvature flow of entire graphsHuisken's theoremMean convex mean curvature flowMonotonicity formulaeSingularity analysisNoncollapsingSelf-similar solutionsAncient solutionsGauss curvature flowsThe affine normal flowFlows by superaffine powers of the Gauss curvatureFully nonlinear curvature flowsFlows of mean curvature typeFlows of inverse-mean curvature typeBibliographyIndex

This textbook, written by four experts in the field, offers an authoritative introduction and overview to the topic of extrinsic geometric flows. It will serve well as a primary text for a graduate student who already has background knowledge of differential geometry and (some) partial differential equations. It will also serve as a useful reference for experts in the field."" - John Ross, Southwestern University