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Geometric measure theory, fall 2014

Lecturer

Pertti Mattila

Scope

10 sp.

Type

Advanced studies

Prerequisites   

Basic knowledge of measure and integration theory such as the courses "Mitta ja integraali" and "Reaalianalyysi I". "Reaalianalyysi II" is useful but not necessary.

Lectures

Weeks 36-42 and 44-50, Wednesday 14-16 in room B322 and Thursday 14-16 in room C122.

The first lecture is on Wednesday, September 3. On Thursday, September 4, there will be no lecture.

The last two weeks:

Lectures normally on December 3 and 4.

Thursday, December 4, 16-18, CK111: Joni Teräväinen: Marstrand's projection theorem

Change of day:

Thursday (not Wednesday), December 11, 14-16, B322: Laura Venieri: Besicovitch sets

Course description

Geometric measure is an area of mathematics where measure theoretic methods are used to study geometric properties of many different kinds of objects. These include generalized surfaces (rectifiable sets, currents, varifolds) and fractals. The field has applications and connections to many branches of mathematics, for example, calculus of variations, partial differential equations, real, complex and harmonic analysis, dynamical systems and probability theory. The topics discussed will include

isoperimetric and isodiametric inequalities,

area and coarea (change of variable) formulas

rectifiable sets and measures

sets of finite perimeter

Lecture notes

Exams

 

Bibliography

L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, 1992.

H. Federer, Geometric Measure Theory, Springer-Verlag, 1969.

P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press, 1995.

F.H. Lin and X. Yang, Geometric Measure Theory, International Press, 2002.

F. Morgan, Geometric Measure Theory, A Beginner's Guide, Academic Press, 1988.

Registration


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Exercises

Exercise sessions on Thursdays 16-18 in CK111. The first will be on September 18.

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

GroupDayTimePlaceTeacher
1.Thursday 16-18 CK111 Pertti Mattila 

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