**UM Math Graduate Students Seminar**

Armando Cabrera

* University of Miami *

**will present**

**The Isoperimetric Inequality and the Curve Shortening Flow **

Friday, October 4, 2013, 2:30pm

Ungar Building Room 402

**Abstract:**One of the oldest theorems in Differential Geometry is the Isoperimetric Inequality, which is related to the Isoperimetric Problem: Of all simple closed curves in the plane with a given length L, which one bounds the largest area? This problem and its solution was known by the Greeks, but the first complete proof of the theorem did not appear until 1870. We will see how we can prove this theorem with elementary calculus. After this, we will introduce the Curve Shortening Flow and obtain the Isoperimetric Inequality from it.

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