Geometric depletion of vortex stretch in 3D viscous incompressible flow

New geometric constraints on vorticity are obtained which suppress possible development of finite-time singularity from the nonlinear vortex stretching mechanism. We find a new condition on the smoothness of the direction of vorticity in the vortical region which yields regularity. We also detect a regularity condition of isotropy type on vorticity in the intensive vorticity region via a new cancellation principle. This is in contrast with the one of isotropy type on the curl of vorticity obtained recently by A. Ruzmaikina and Z. Grujić [A. Ruzmaikina, Z. Grujić, On depletion of the vortex-stretching term in the 3D Navier–Stokes equations, Comm. Math. Phys. 247 (2004) 601–611]. We improve as well all of their results by eliminating their assumption that the initial vorticity ω0 is required to be in L1.