A barrier principle at infinity for varifolds with bounded mean curvature

Locality of the mean curvature of rectifiable varifolds

The aim of this paper is to investigate whether, given two rectifiable k-varifolds in R with locally bounded first variations and integer-valued multiplicities, their mean curvatures coincide H-almost everywhere on the intersection of the supports of their weight measures. This so-called locality property, which is well-known for classical C2 surfaces, is far from being obvious in the context o...

Eigenvalue estimates for submanifolds with locally bounded mean curvature

We give lower bounds estimates for the first Dirichilet eigenvalues for domains Ω in submanifolds M ⊂ N with locally bounded mean curvature. These lower bounds depend on the local injectivity radius, local upper bound for sectional curvature of N and local bound for the mean cuvature of M . For sumanifolds with bounded mean curvature of Hadamard manifolds these lower bounds depends only on the ...

Deformations of constant mean curvature 1/2 surfaces in H × R with vertical ends at infinity

We study constant mean curvature 1/2 surfaces in H × R that admit a compactification of the mean curvature operator. We show that a particular family of complete entire graphs over H admits a structure of infinite dimensional manifold with local control on the behaviors at infinity. These graphs also appear to have a half-space property and we deduce a uniqueness result at infinity. Deforming n...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Currents and Flat Chains Associated to Varifolds, with an Application to Mean Curvature Flow

We prove under suitable hypotheses that convergence of integral varifolds implies convergence of associated mod 2 flat chains and subsequential convergence of associated integer-multiplicity rectifiable currents. The convergence results imply restrictions on the kinds of singularities that can occur in mean curvature flow.