Quantitative rigidity estimates
Quantitative rigidity estimates

Camillo De Lellis , University of Zurich
Rutgers  Hill Center, Room 425
For many classical rigidity questions in differential geometry it is natural to ask to which extent they are stable. I will review several recent results in the literature. A typical example is the following: there is a constant $C$ such that, if $\Sigma$ is a $2$dimensional embedded closed surface in $R^3$, then $\min_\lambda \A \lambda g\_{L^2} \leq C \A  {\rm tr A} g/2\_{L^2}$, where $A$ is the second fundamental form of the surface and $g$ the Riemannian metric as a submanifold of $R^3$.