On conditions for unrectifiability of a metric space

We find necessary and sufficient conditions for a Lipschitz map $f:\mathbb{R}E\to X$, into a metric space to have the image with the $k$-dimensional Hausdorff measure equal zero, $H^k(f(E))=0$. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a variant of the classical implicit function theorem. Applications include pure unrectifiability of the Heisenberg groups and that of more general Carnot-Carath\'eodory spaces

Light plasmon mode in the CFL phase

The self-energies and the spectral densities of longitudinal and transverse gluons at zero temperature in the color-flavor-locked (CFL) phase are calculated. There appears a collective excitation, a light plasmon, at energies smaller than two times the gap parameter and momenta smaller than about eight times the gap. The minimum in the dispersion relation of this mode at some nonzero value of momentum corresponds to the van Hove singularity.Comment: 4 pages, 4 figures, Talk given by H. Malekzadeh, to appear in the proceedings of the conference "Quark Confinement and the Hadron Spectrum VII" (QCHS7), Ponta Delgada, 2 - 7 September 200