5 papers
Regularity estimates of a fluid-free surface evolution
Malte Kampschulte, Joonas Niinikoski, Sebastian Schwarzacher
In this work the evolution of a fluid droplet in vacuum is considered. This means that the surface tension and the fluid forces are in equilibrium at the free boundary. The fluid i…
Consistency of the flat flow solution to the volume preserving mean curvature flow
Vesa Julin, Joonas Niinikoski
We consider the flat flow solution, obtained via discrete minimizing movement scheme, to the volume preserving mean curvature flow starting from C^{1,1}-regular set. We prove the c…
Stationary sets of the mean curvature flow with a forcing term
Vesa Julin, Joonas Niinikoski
We consider the flat flow approach for the mean curvature equation with forcing in an Euclidean space of dimension at least 2. Our main results states that tangential…
Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow
Vesa Julin, Joonas Niinikoski
We prove a new quantitative version of the Alexandrov theorem which states that if the mean curvature of a regular set in R^{n+1} is close to a constant in L^{n}-sense, then the se…
Volume preserving mean curvature flows near strictly stable sets in flat torus
Joonas Niinikoski
In this paper we establish a new stability result for the smooth volume preserving mean curvature flow in flat torus in low dimensions . The result says roughl…