Let M be a compact Riemannian manifold. For x, y G M, denote by p(x,y) the distance between x and y, i.e., the infimum of lengths of continuous piecewise C paths between x and y. (Notice that for geodesically complete manifolds there is always a path from x to y of length p(x,y).) The invariants of M based on the distance p are called metrical invariants. Most of them are related to the geometr...

Given a closed m-dimensional manifold M immersed in R, we estimate its diameter d in terms of its mean curvature H by

Diameter of IVC on CT axial section is a important predictor of hypotension in blunt abdominal trauma. CT scan of abdomen is usually requested whenever there is hemoperitoneum/ free fluid noted on FAST USG imaging in emergency department. The diameter of IVC was measured at infrarenal part. In our review of 25 cases of MDCT abdomen in blunt abdominal trauma, 40% of the cases had FIVC and there ...