Continuity and asymptotic limit of the Weyl-law constant for the p-Laplacian

Let $M$ be a closed $n$-dimensional Riemannian manifold, let $p$ be the exponent in the $p$-Laplacian, and let $c_n(p)$ be the universal constant in the asymptotic law

$$\lim_{\xi \to \infty} \frac{ \# \{k \ge 1 \mid \lambda_{k,p}(M)^{1/p} < \xi \}}{\xi^n} = c_n(p) \operatorname{vol}_g(M).$$

Here $\circledcirc_n$ denotes the Euclidean packing constant. Continuity and asymptotic-limit conjecture. The function $c_n(p)$ is continuous in $p$ and

$$\lim_{p \to \infty} c_n(p) = \circledcirc_n.$$

This conjecture links the asymptotic eigenvalue distribution of the $p$-Laplacian with the asymptotic law for packing radii. The source provides no resolution, so the continuity and limiting behavior remain open.