## Classical and New Problems in Geometric Analysis

In the first part of the talk, we will review the classical

Alexandrov Theorem, the Isoperimetric Inequality and the Willmore

Inequality in Euclidean spaces, trying to highlight their mutual

connections and to discuss how they can be proved through PDE's

techniques.

In the second part of the talk we will consider these problems in

relevant families of Riemannian manifolds, approaching the frontier of

modern research on these topics.