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. Gruji? A. Ruzmaikina, Z. Gruji?, 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.