In this paper, we establish two families of sharp geometric inequalities for closed hypersurfaces in space forms or other warped product manifolds. Both compare three distinct quantities. The first family concerns the k-th boundary momentum, area and weighted volume, has applications to Weinstock-type Steklov Wentzell eigenvalues on star-shaped mean convex domains. This generalizes main results...

We investigate the topology of complete Riemannian manifolds with the radial curvature at the base manifold bounded below by those of model surfaces. Here, model surfaces are generalized surfaces of revolution and warped product models which are diffeomorphic to S.

In this paper, the geometry of F -invariant CR-submanifolds of a Kaehlerian product manifold is studied. Fundamental properties of this type submanifolds are investigated such as CR-product, D⊥-totally geodesic and mixed geodesic submanifold. Finally, we have researched totally-umbilical F -invariant proper CR-submanifolds and CR-products in a Kaehlerian product manifold M = M1(c1)×M2(c2) M.S.C...

Contact resonance atomic force microscopy (CR-AFM) methods currently utilize the eigenvalues, or resonant frequencies, of an AFM cantilever in contact with a surface to quantify local mechanical properties. However, the cantilever eigenmodes, or vibrational shapes, also depend strongly on tip-sample contact stiffness. In this paper, we evaluate the potential of eigenmode measurements for improv...