| Abstract
| - Full-sky microwave surveys like the upcoming Planck satellite mission will detect of order 10 4 galaxy clusters through their thermal Sunyaev-Zel'dovich effect. I investigate the properties of the gravitationally lensing subsample of these clusters. The main results are: (1) The combined sample comprises $\ga$70% of the complete sample. (2) It is confined to redshifts $0.2\pm0.1$, and to masses $(5\pm3) 10^{14} M_odot$. (3) Using a particular measure for the weak lensing effect, viz. the aperture mass, cluster masses can be determined with a relative accuracy of ~20% if their density profile is known. Consequently, the mass function of the combined sample can accurately be measured. (4) For low-density universes, I predict a sharp peak in the measured (aperture) mass function near $5 10^{14} M_odot$ and explain its origin, showing that the peak will be absent in high-density universes. (5) The location of the peak and the exponential decrease of the mass function on its high-mass side will allow the determination of the amplitude of the dark-matter power spectrum on the cluster scale and the baryon fraction in clusters, and constrain the thermal history of the intracluster gas.
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