## UC Berkeley / Lawrence Berkeley Laboratory

#### Stability results for some isoperimetric problems

**Carlo Nitsch, University of Naples, Federico II**

##### February 22nd, 2010 at 2PM–3PM in 740 Evans Hall [Map]

An isoperimetric problem usually consists in optimizing a given
domain-dependent functional possibly subject to some additional geometrical
constraints on the domain. In this talk I will focus on two well-known examples
of isoperimetric problems:

- Lord Rayleigh's conjecture (1877) – The principal tone of a
drum of fixed area is the least possible when the drum has a circular
shape.
- St Venant's conjecture (1856) – Among all solid bars with the
same cross-sectional area, the circular shaft gives the maximal
torsional rigidity.

In particular I will discuss some recent results concerning quantitative
versions of both these conjectures.