We give a coadjoint orbit's diffeomorphic deformation between the classical semisimple case and semi-direct product given by Cartan decomposition. The two structures admit Hermitian symplectic form defined in complex Lie algebra. provide some applications such as constructions of Lagrangian submanifolds.

Using a simplified version of Kuranishi perturbation theory that we call semi-global structures, give definition the equivariant Lagrangian Floer cohomology pair submanifolds are fixed under finite symplectic group action and satisfy certain simplifying assumptions.

The Douglas–Rachford (DR) and alternating direction method of multipliers (ADMM) are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local linear convergence behaviour of DR/ADMM when the involved functions are moreover partly smooth. More...

In this paper, we consider semi-slant submanifolds in a locally conformal Kaehler manifold and space form. We give inequalities for the length of second fundamental form mean curvature and, using Gauss Codazzi equations, get many useful results

Abstract. In this paper we establish a gap phenomenon for immersed surfaces with arbitrary codimension, topology and boundaries that satisfy one of a family of systems of fourth-order anisotropic geometric partial differential equations. Examples include Willmore surfaces, stationary solitons for the surface diffusion flow, and biharmonic immersed surfaces in the sense of Chen. On the boundary ...