Small-ball spectral convergence for sub-Riemannian diffusions

A sub-Riemannian diffusion killed when it exits a sufficiently small metric ball is expected to exhibit an analogous small-ball spectral convergence to the corresponding nilpotent or tangent diffusion. Small-ball spectral convergence conjecture. A similar result should hold for more general sub-Riemannian diffusions killed at exiting a small metric ball. This would extend the convergence of the re-normalized Dirichlet eigenvalues established here for small balls in $\operatorname{SU}(2)$ to a broader class of sub-Riemannian diffusions, but the source does not specify the precise hypotheses or formulate the corresponding limiting spectrum.