We study transverse conformal Killing forms on foliations and prove a Gallot-Meyer theorem for foliations. Moreover, we show that on a foliation with C-positive normal curvature, if there is a closed basic 1-form φ such that ∆Bφ = qCφ, then the foliation is transversally isometric to the quotient of a q-sphere.

This paper is devoted to the modeling of real textured images by functional minimization and partial differential equations. Following the ideas of Yves Meyer in a total variation minimization framework of L. Rudin, S. Osher, and E. Fatemi, we decompose a given (possible textured) image f into a sum of two functions u+v, where u ¥ BV is a function of bounded variation (a cartoon or sketchy appr...