Department of Mathematics

Topics on Analysis on Metric Spaces

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Lecturer: Andrea Schioppa Lectures: Mondays 15-17 @ HG E 1.1

First lecture: Monday, 16/02/2015.

Course Description

This course will illustrate some aspects of geometric measure theory in metric spaces, in particular results that can be classified as "0-order calculus" (e.g. estimates for the maximal functions) and "first-order calculus" (e.g. differentiation of Lipschitz functions).

A list of references, notes and topics covered during the lectures will be updated throughout the course.


A tentative outline:
* Hausdorff measures
* Doubling measures and differentiation of measures
* Rectifiable sets in metric spaces and metric differentiation
* Poincare' inequalities via upper gradients
* Generalizations of Rademacher's Theorem
* Applications to metric embeddings


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© 2016 Mathematics Department | Imprint | Disclaimer | 15 February 2015