Integrative teaching
Exercises
Examination procedure
Oral exam and seminars
Prerequisites
Familiarity with functional analysis, elliptic and parabolic equations, and theory
of hypersurfaces. Some review will be made anyway.
The course is recommended for students of any year of Ph.D., and for students of the fifth year of the undergraduate course.
Syllabus
Local existence for parabolic systems
Curvature motion in the plane
Review of hypersurface geometry
Mean curvature flow
Evolution of convex sets
Grayson's Theorem
Time permitting: formation of singularities and geometric applications
Bibliographical references
Friedman, Avner Partial differential equations of parabolic type. Prentice-Hall, Inc., Englewood Cliffs, N.J. 1964
Mantegazza, Carlo Lecture notes on mean curvature flow. Progress in Mathematics, 290. Birkhäuser/Springer Basel AG, Basel, 2011.
Zhu, Xi-Ping Lectures on mean curvature flows. AMS/IP Studies in Advanced Mathematics, 32. American Mathematical Society, Providence, RI; International Press, Somerville, MA, 2002.