Geometry and Topology Seminar: The Lévy-Gromov Isoperimetric Inequality
16 March 2017 13:00 in CM221
The isoperimetric inequalities are mathematical responses to centuries-old problems. For example, the Ancients already knew that to construct a surface-maximal city while having a limited amount of resources for the ramparts, they had to give a circular shape to the fortifications. Mathematically well-formulated, this is the essence of all isoperimetric inequalities, see https://en.wikipedia.org/wiki/Isoperimetric_inequality
In this talk, we will explore the famous Levy-Gromov isoperimetric inequality, which is a generalisation of this problem to a compact Riemannian manifold with some curvature assumptions. We will follow Gromov’s proof dating back to 1986 and give some physical and mathematical applications.
This talk will be accessible to a wide audience and to students.