# On the geometric properties of rectifiable sets

Università degli Studi Trento

38123 Povo (TN)

Tel +39 04 61/281508-1625-1701-3786

dept.math [at] unitn.it

**Venue**: Seminar Room "-1" - Department of Mathematics – Via Sommarive, 14 - Povo Trento

**Hour**: 11.00 a.m.

**Le Van Phu Cuong**- PhD in Mathematics

**Abstract**:

Rectifiable sets are the fundamental objects of studying in geometric measure theory. It is an extension of the idea of a rectifiable curve to higher dimensions and it has many of the desirable properties of smooth manifolds. Infact, in this talk we are first devoted to proving the existence of the approximate tangent spaces that are defined almost everywhere in a suitable sense. Then, we prove the important result that countable n-rectifiable sets are essentially characterized by the property of having the approximate tangent space almost everywhere in terms of measure-theoretic properties.

The seminar corresponds to the final exam of Geometric Measure Theory, a planned course within Le Van Phu Cuong's first year PHD study programme

Contact person: **Francesco Serra Cassano**