# 401-4115-00L Introduction to Geometric Measure Theory

Semester | Autumn Semester 2018 |

Lecturers | U. Lang |

Periodicity | non-recurring course |

Language of instruction | English |

### Courses

Number | Title | Hours | Lecturers | |||||||
---|---|---|---|---|---|---|---|---|---|---|

401-4115-00 V | Introduction to Geometric Measure Theory | 3 hrs |
| U. Lang |

### Catalogue data

Abstract | Introduction to Geometric Measure Theory from a metric viewpoint. Contents: Lipschitz maps, differentiability, area and coarea formula, rectifiable sets, introduction to the (de Rham-Federer-Fleming) theory of currents, currents in metric spaces after Ambrosio-Kirchheim, normal currents, relation to BV functions, slicing, compactness theorem for integral currents and applications. |

Objective | |

Content | Extendability and differentiability of Lipschitz maps, metric differentiability, rectifiable sets, approximate tangent spaces, area and coarea formula, brief survey of the (de Rham-Federer-Fleming) theory of currents, currents in metric spaces after Ambrosio-Kirchheim, currents with finite mass and normal currents, relation to BV functions, rectifiable and integral currents, slicing, compactness theorem for integral currents and applications. |

Literature | - Pertti Mattila, Geometry of Sets and Measures in Euclidean Spaces, 1995 - Herbert Federer, Geometric Measure Theory, 1969 - Leon Simon, Introduction to Geometric Measure Theory, 2014, Link - Luigi Ambrosio and Bernd Kirchheim, Currents in metric spaces, Acta math. 185 (2000), 1-80 - Urs Lang, Local currents in metric spaces, J. Geom. Anal. 21 (2011), 683-742 |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 6 credits |

Examiners | U. Lang |

Type | session examination |

Language of examination | English |

Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |

Mode of examination | oral 20 minutes |

Additional information on mode of examination | Prüfungssprache: Deutsch oder Englisch / Language of examination: English or German |

This information can be updated until the beginning of the semester; information on the examination timetable is binding. |

### Learning materials

No public learning materials available. | |

Only public learning materials are listed. |

### Groups

No information on groups available. |

### Restrictions

There are no additional restrictions for the registration. |

### Offered in

Programme | Section | Type | |
---|---|---|---|

Mathematics Bachelor | Selection: Analysis | W | |

Mathematics Master | Selection: Analysis | W |