Geometric Measure Theory.

Inst. för Matematik | KTH |

Geometric Measure Theory

Reading Course 7.5hp

November 2014 – March 2015

(Study periods 2-3.)

Instructions for th e exam seminar can be found here.

The poor excuse for a Teacher: John Andersson

First Meeting: November 6^th at 10:15 in Room 3733

Course description: Follow this link.

Course Literature: After much consideration I have decided that we will use:

Author: Leon Simon

Title: Lectures on Geometric Measure Theory.

That is a standard text that covers much material in few pages. The downside is that it is typeset in the old style (difficult to read). Something that is compensated by that you you can find it for free here at the publishers homepage.

Other books that might be of help is Francesco Maggi “Sets of finite perimeter and geometric variational problems.” or E. Giusti “Minimal Surfaces and Functions of Bounded Variation”.

Course plan: This is a reading course and we will not have any traditional lectures. However, we will have informal seminars every other week. The seminars are planed to last for around an hour (never longer than 2 hours) and we will begin with someone (either me or more often by a course participant) giving a brief summary of this weeks reading. This will be followed by a group discussion where we try to situate the material within field, understand the ideas and motivations for the ideas.

Seminar	Date, Room 3733 10am-12pm	Reading in Simon	Responsible person. All email addresses are @kth.se	Documents
1	November 6^th 2014	Basic theory. pp 1-28	Name: John Andersson Email: johnan	Questions Slides
2	November 20^th 2014	Lipschtz & BV-functions, submanifolds, pp. 29-46	Name: Thomas Ohlson Timoudas Email: ttohlson
3	December 4^th 2014	Area & coarea formulas and 1^st-2^nd variation, pp 46-57	Name: Andreas Minne email: minne	Questions
4	December 18^th 2014	Rectifiable sets, pp 58-70	Name: Gohar Aleksanyan email: galeksan	Questions
5	January 15^th 2015	pp 70-80	Name: Eric Larsson email: ericlar	Questions Erik's Notes Example From Seminar 5
6	January 29^th 2015	pp 80-89	Name: Simon Larson email: simla	Questions
7	February 12^th 2015	Pp 89-101	Name: Erik Duse email: duse	Questions
8	February 26^th 2015	Pp 102-120	Name: John Andersson email: johnan	Questions
9	March 12^th 2015	Pp 120-129	Name: Gohar Aleskanyan email: galeksan	Questions “Map” of chapter 5.

Examination: I have no intention of being very strict in this course. The material is difficult and I expect the course participants to be motivated. Active participation in most of the seminars will be requited. But if you have legit reasons for missing one or a few seminars (such as going to conferences or teaching) you will still be able to pass. However, every participant will have to introduce one seminar with a 20 minute presentation of the most important aspects of that weeks reading. The course will end with an exam seminar. Instructions for the exam seminar can be found here.


Avdelning Matematik	Sidansvarig: John Andersson Uppdaterad: 2014-09-27