The celebrated Curvature-Dimension condition CD(K,N) of Bakry and Emery is a well-known generator of isoperimetric, functional and concentration inequalities. Traditionally, the range of admissible values for the generalized dimension N has been confined to [n,\infty], where n is the (topological) dimension of the ambient space. We extend this in two manners.
First, we treat the range N
Second (time permitting), to treat the forbidden range 1