A surface $\Sigma $ in the hyperbolic space $\h^ 3$ is called a horo-shrinker if its mean
curvature $ H $ satisfies $ H=\langle N,\partial_z\rangle $, where $(x, y, z) $ are the …

In this paper, the motion of inverse mean curvature flow which starts from a closed star-
sharped hypersurface in special rotationally symmetric spaces is studied. It is proved that the …

Geometric flows have many applications in physics and geometry. The mean curvature flow
occurs in the description of the interface evolution in certain physical models. This is related …

We study translators of the mean curvature flow in the product space H 2× R. In H 2× R there
are three types of translations: vertical translations due to the factor R and parabolic and …

The mean curvature flow is the most natural way to deform a hypersurface according to its
curvature, since it evolves the parametrization by means of the heat equation. In 1987, G …

We study the convergence of axially symmetric hypersurfaces evolving by volume-
preserving mean curvature flow. Assuming the surfaces do not develop singularities along …

We study the area preserving curve shortening flow with Neumann free boundary conditions
outside of a convex domain in the Euclidean plane. Under certain conditions on the initial …

We obtain estimates on nonlocal quantities appearing in the volume preserving mean
curvature flow (VPMCF) in the closed, Euclidean setting. As a result we demonstrate that …

In a rotationally symmetric space\overline M around an axis A (whose precise definition is
satisfied by all real space forms), we consider a domain G limited by two equidistant …

This paper concerns closed hypersurfaces of dimension $ n (\geq 2) $ in the hyperbolic
space ${\mathbb {H}} _ {\kappa}^{n+ 1} $ of constant sectional curvature $\kappa $ evolving …