arXiv subjects

Maria Athanassenas

Publications and source records attributed to Maria Athanassenas.

3 recordsLinked to original sources

arXiv2019

Singularities of Axially Symmetric Volume Preserving Mean Curvature Flow

We investigate the formation of singularities for surfaces evolving by volume preserving mean curvature flow. For axially symmetric flows - surfaces of revolution - in $\mathbb{R}^3$ with Neumann boundary conditions, we prove that the first developing singularity is of Type I. The result is obtained without any additional curvature assumptions being imposed, while axial symmetry and boundary conditions are justifiable given the volume constraint. Additional results and ingredients towards the main proof include a non-cylindrical parabolic maximum principle, and a series of estimates on geometric quantities involving gradient, curvature terms and derivatives thereof. These hold in arbitrary dimensions.

math.DG↗

arXiv2011

On the Convergence of Axially Symmetric Volume Preserving Mean Curvature Flow

We study the convergence of an axially symmetric hypersurface evolving by volume preserving mean curvature flow. Assuming the surface is not pinching off along the axis at any time during the flow, and without any additional conditions, as for example on the curvature, we prove that it converges to a hemisphere, when the hypersurface has a free boundary and satisfies Neumann boundary data, and to a sphere when it is compact without boundary.

math.DG↗

arXiv2006

The Capillarity Problem for Compressible Liquids

In this paper we study existence and regularity of solutions to the capillarity problem for compressible liquids in a tube. We introduce an appropriate space of functions of bounded variation, in which the energy functional recently introduced by Robert Finn can be defined. We prove existence of a locally Lipschitz minimiser in this class.

math.AP↗