- No lectures (nor home work classes) during weeks 43 (25-26.10) and 44 (1-3.11).
Weeks 36-42 and 44-50, Tuesday 12-14 and Thursday 10-12 in room C124. Note: No lectures (nor home work classes) during weeks 43 (25-26.10) and 44 (1-3.11).
Between 9.11 - 14.12 we will have extra classes/home work sessions on Wednesdays 12-14 in room B322.
The course can be passed by anor preferably by giving presentations in the home work classes and writing essays.
How to pass the course by giving presentations? The plan is that a student gives two presentations (1-2 hours each) on a chosen topic and writes an essay on the topic (and, of course, follows the presentations of others).
L. Evans and R. Gariepy: Measure theory ans fine properties of functions, CRC Press, 1992.
H. Federer: Geometric Measure Theory, Springer, 1969.
F. Lin and X. Yang: Geometric Measure Theory: An Introduction, International Press, 2002.
P. Mattila: Geometry of sets and measures in Euclidean spaces, Cambridge University Press,1995.
F. Morgan: Geometric Measure Theory, A Beginner's Guide, Academic Press, 1987. An e-book available for students of UH.
P. Mattila: Currents and varifolds. Hand-written lecture notes, fall 2011.
I. Holopainen: Geometric measure theory (first 88 pages + appendix). Proof of the Deformation theorem, discussions on regularity results (stationary varifolds, mass minimizing currents) will be added later.
Did you forget to register? What to do?
- Exercises 1 Solutions 1
- Exercises 2 Solutions 2
- 28.9.2016, Presentation on the Riesz representaton theorem by Ville Marttila (see Appendix in the lecture notes)
- 5.10.2016, Presentation on weak convergence of measures and on the compactness of Radon measures by Janne Siipola (see Appendix in the lecture notes)
- 12.10.2016, Presentation on Rademacher's theorem by Akseli Haarala
- 19.10.2016, Presentation on the area formula by Krishnan Narayanan
- 8.11.2016 (Tuesday), Presentation on the co-area formula by Otte Heinävaara
- 9.11.2016, Presentation on the Whitney extension by Valter Lillberg
- 9.11.2016, by Ville Karlsson
- 16.11.2016, Presentation on approximate tangent spaces and on rectifiable sets (part I) by Ville Marttila
- 16.11.2016, Presentation on approximate tangent spaces and on rectifiable sets (part II) by Janne Siipola
- 23.11.2016, Presentation on the monotonicity formula and isoperimetric inequality by Akseli Haarala
- 23.11.2016, Presentation on the rectifiability theorem and tangent cones (part I) by Krishan Narayanan
- 30.11.2016, Presentation on the rectifiability theorem and tangent cones (part II) by Otte Heinävaara
- 30.11.2016, Presentation on the regularity theory (part I) by Valter Lillberg
- 7.12.2016, Presentation on the regularity theory (part II) by Ville Karlsson
Course feedback can be given at any point during the course. Click here.