We apply multivariate tensor-based morphometry to study lateral ventricular surface abnormalities associated with HIV/AIDS. We use holomorphic one-forms to obtain a conformal parameterization of ventricular geometry, and to register lateral ventricular surfaces across subjects. In a new development, we computed new statistics on the Riemannian surface metric tensors that encode the full information in the deformation tensor fields. We applied this framework to 3D brain MRI data, to map the profile of lateral ventricular surface abnormalities in HIV/AIDS (11 subjects). Experimental results demonstrated that our method powerfully detected brain surface abnormalities. Multivariate Hotelling's T 2 statistics on the local Riemannian metric tensors, computed in a log-Euclidean framework, detected group differences with greater power than other surface-based statistics including the Jacobian determinant, largest and least eigenvalue, or the pair of eigenvalues of the Jacobian matrix. Computational anatomy studies may therefore benefit from surface parameterization using differential forms and tensor-based morphometry, in the log-Euclidean domain, on the resulting surface tensors.