Short-Time Existence Theorem for the CR Torsion Flow

In this paper, we study the torsion flow which is served as the CR analogue of the Ricci flow in a closed pseudohermitian manifold. We show that there exists a unique smooth solution to the CR torsion flow in a small time interval with the CR pluriharmonic function as an initial data. In spirit, it is the CR analogue of the Cauchy-Kovalevskaya local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problemsComment: 30 page

Legendrian mean curvature flow in η\eta-Einstein Sasakian manifolds

Recently, there are a great deal of work done which connects the Legendrian isotopic problem with contact invariants. The isotopic problem of Legendre curve in a contact 3-manifold was studies via the Legendrian curve shortening flow which was introduced and studied by K. Smoczyk. On the other hand, in the SYZ Conjecture, one can model a special Lagrangian singularity locally as the special Lagrangian cones in C^{3}. This can be characterized by its link which is a minimal Legendrian surface in the 5-sphere. Then in these points of view, in this paper we will focus on the existence of the long-time solution and asymptotic convergence along the Legendrian mean curvature flow in higher dimensional {\eta}-Einstein Sasakian (2n+1)-manifolds under the suitable stability condition due to the Thomas-Yau conjecture.Comment: arXiv admin note: text overlap with arXiv:0906.5527 by other author

IMAGE-BASED MEASUREMENT AND BIOMECHANICAL ANALYSIS OF THE KNEE JOINT DURING FUNCTIONAL ACTIVITIES

A new approach based on the integration of medical image-based measurement techniques, infrared stereophotogrammetry and finite element modelling (FEM) was developed for comprehensive subject-specific biomechanical analyses of the knee joint during weight-bearing functional activities including cycling. The medical image-based methods include digitally reconstructed radiograph (DRR) based 3D fluoroscopy methods, and a new slice-to-volume registration method using FLASH MRI for the real-time measurement of the 3D kinematics of the knee in vivo. With the new approach, the soft tissue artefacts associated with skin marker-based stereophotogrammetry and their effects on the calculated biomechanical variables were also investigated