Introduction 1 1. A review of the Hilbert manifold of maps and diffeomorphism groups 5 1.1. Notation 7 2. New diffeomorphism subgroups 8 2.1. Neumann boundary conditions for diffeomorphisms 8 2.2. Mixed boundary conditions for diffeomorphisms 12 2.3. Dirichlet boundary conditions for diffeomorphisms 14 2.4. The group exponential map 14 2.5. A unified approach to differentiable structure on subg...

We investigate the fundamental conditions on the sampling pattern, i.e., locations of the sampled entries, for finite completability of a low-rank tensor given some components of its Tucker rank. In order to find the deterministic necessary and sufficient conditions, we propose an algebraic geometric analysis on the Tucker manifold, which allows us to incorporate multiple rank components in the...

In this paper, we study a geometric G^2 Hermite interpolation by planar rational cubic Bézier curves. Two data points, two tangent vectors and two signed curvatures interpolated per each rational segment. We give the necessary and the sufficient intrinsic geometric conditions for two C^2 parametric curves to be connected with G2 continuity. Locally, the free parameters w...