Let (Mn, g), n ≥ 4, be a compact simply-connected Riemannian manifold with nonnegative isotropic curvature. Given 0 < l ≤ L, we prove that there exists ε = ε(l, L, n) satisfying the following: If the scalar curvature s of g satisfies l ≤ s ≤ L and the Einstein tensor satisfies |Ric − s n g| ≤ ε then M is diffeomorphic to a symmetric space of compact type. This is a smooth analogue of the result...

In this paper we solve the Plateau problem for spacelike surfaces with constant mean curvature in Lorentz-Minkowski three-space L and spanning two circular (axially symmetric) contours in parallel planes. We prove that rotational symmetric surfaces are the only compact spacelike surfaces in L of constant mean curvature bounded by two concentric circles in parallel planes. As conclusion, we char...

The Gaussian curvature tern in the expression for the energy density in bending of a lipid bilayer can be decomposed in two terns one symmetric and the other one antisymmetric in the principal curvatures. The symmetric tern is proportional to the square of the mean local curvature. A similar tern has exclusively been used to calculate the equilibrium shape of bilayer structures the topology of ...

In this paper, we discuss gravitational collapse of spherically symmetric spacetimes. We derive a general formalism by taking two arbitrary spherically symmetric spacetimes with g00 = 1. Israel’s junction conditions are used to develop this formalism. The formulae for extrinsic curvature tensor are obtained. The general form of the surface energy-momentum tensor depending on extrinsic curvature...