PLANS: Arrive Wednesday evening, leave Sunday morning.
----------------------------------------------------------------------------
TALK: Friday, Sep 17, 2-3:30pm in Ker 228
Cases of Equality for the Gaussian Isoperimetric
and Rearrangement Inequalities
ABSTRACT:
We determine all the cases of equality in a recent inequality due to
S. Bobkov. Since the isoperimetric inequality for R^n equipped
with Gaussian measure is a consequence of Bobkov's inequality, the result
supplies the cases of equality for this isoperimetrc inequality as well.
As in the more familiar setting of R^n with Lebesgue measure, the
`sharp' form of the isoperimetric inequality on Gauss space gives rise
to a `sharp' rearrangement inequality for functionals which involve an
energy arising from a gradient. A typical example is an energy of
the form
\int |grad u|^2 d\gamma ,
where \gamma is the Gaussian measure on R^n .