Suppose we have two strictly convex closed curves $C\_{1}$ and $C\_{2}$, $C\_{1}$ contains $C\_{2}$, 
then can we conclude $\int\_{C\_{1}} \kappa\_{1}^{p} ds\geq \int\_{C\_{2}} \kappa\_{2}^{p} ds$, $\kappa\_{1}$ and $\kappa\_{2}$ are corresponding curvatures of $C\_{1}$ and $C\_{2}$, 
$p$ is between 0 and 1



a question about Lp norm of curvature on convex curves
No. Let $C\_2$ be the unit circle and $C\_1$ be a big square with corners rounded off by circle arcs of radius $r\ll 1$. The integral for $C\_2$ is the same as for the $r$-circle and this is very small.


