Let M0 be a compact, regular q-pseudoconcave compact CR submanifold of a complex manifold G and B a holomorphic vector bundle on G such that dimH ( M0,B ∣∣ M ) = 0 for some fixed r < q. We prove a global homotopy formula with C estimates for r-cohomology of B on arbitrary CR submanifold M close enough to M0.

We propose a unified computational framework for the problem of deformation and rigidity of submanifolds in a homogeneous space under geometric constraint. A notion of 1-rigidity of a submanifold under admissible deformations is introduced. It means every admissible deformation of the submanifold osculates a one parameter family of motions up to 1st order. We implement this idea to the question...

‎Based on a definition for circle in Finsler space‎, ‎recently proposed by one of the present authors and Z‎. ‎Shen‎, ‎a natural definition of extrinsic sphere in Finsler geometry is given and it is shown that a connected submanifold of a Finsler manifold is totally umbilical and has non-zero parallel mean curvature vector field‎, ‎if and only if its circles coincide with circles of the ambient...

Given a control-affine system and a controlled invariant submanifold, we present necessary and sufficient conditions for local feedback equivalence to a system whose dynamics transversal to the submanifold are linear and controllable. A key ingredient used in the analysis is the new notion of transverse controllability indices of a control system with respect to a set.

Let G be a definably compact definable C group and 1 ≤ r < ∞. Let X be a definable CG submanifold of a representation of G and Y a definable C submanifold of R. We prove that every G invariant surjective submersive definable C map f : X → Y is piecewise definably CG trivial.

background: using primary tumor gene expression has been shown to have the ability of finding metastasis-driving gene markers for the prediction of breast cancer recurrence (bcr). however, there are some difficulties associated with the analysis of microarray data which led to poor predictive power and inconsistency of the previously introduced gene signatures. methods: in this study a hybrid m...

By applying the spectral decomposition of a submanifold of a Euclidean space, we derive several sharp geometric inequalities which provide us some best possible relations between volume, center of mass, circumscribed radius, inscribed radius, order, and mean curvature of the submanifold. Several of our results sharpen some well-known geometric inequalities.

A Hamiltonian stationary Lagrangian submanifold of a Kähler manifold is a Lagrangian submanifold whose volume is stationary under Hamiltonian variations. We find a sufficient condition on the curvature of a Kähler manifold of real dimension four to guarantee the existence of a family of small Hamiltonian stationary Lagrangian tori. Mathematics Subject Classification (2000) 58J37 · 35J20 · 35J48...

A unifying definition of trapped submanifold for arbitrary codimension by means of its mean curvature vector is presented. Then, the interplay between (generalized) symmetries and trapped submanifolds is studied, proving in particular that (i) stationary spacetimes cannot contain closed trapped nor marginally trapped sub-manifolds S of any codimension; (ii) S can be within the subset where ther...