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.