Let $(M,g)$ be  a compact Riemannian manfold with $dim M=n$. This gives us  a unique sympletic 

structure $(TM, \omega)$ and a unique volum form $\Omega=\omega^{n}$ on $TM$.

For every $r>0$, let $D_{r}(M)$ be the open Disc bundle on $M$, with radius $r$. Namely $D_{r}(M)$

is the subset of $TM$ which contains all vectors with length  $<r$.

Define:

 ${C(r)=(\text{sympletic capacity of $D_{r}(M)$}})^{2n}$


  $V(r)$=The Volum  of $D_{r}(M)$ with respect to $\Omega$

Question :

>1)Does  $\lim_{r\to \infty} C(r)/V(r)$ exist?    And what is its geometric interpretation?


>2)Does   $\lim_{r\to 0} C(r)/V(r)$ exist?    And what is its geometric interpretation?



Note that the symplectic capacity of  a sympletic manifold $N$of dimension 2n defined as follows:

$\sup\; \{\rho \mid \text{there is  a symplectic embedding from $B_{\rho}(0)\subset \mathbb{R}^{2n}$ to $N$}\}$.

By $B_{\rho}(0)$  I mean the disc around the origin with radius $\rho$.