The open profile thin elastic wavy shell natural oscillations problem is considered. proposed method for determining the numerical values of lowest frequencies and corresponding forms vibrations shells with a complicated shape based on Rayleigh-Ritz energy method. results calculation rigidly pinched lower contour are presented.

We prove vanishing theorems for the kernel of Sampson Laplacian, acting on symmetric tensors a Riemannian manifold and estimate its first eigenvalue negatively pinched manifolds. Some applications these results to conformal Killing are presented.

In a complete simply connected Riemannian manifold X of pinched negative curvature, we give a sharp criterion for a subset C to be the ǫ-neighbourhood of some convex subset of X, in terms of the extrinsic curvatures of the boundary of C. 1

We prove the central limit theorem of random variables induced by distances to Brownian paths and Green functions on universal cover Riemannian manifolds finite volume with pinched negative curvature. further provide some ergodic properties motions an application dynamics geodesic flows in