28 citations · 41 across the 17 of their papers we have counts for
4 papers · 1 filter
Minimizing movements for the generalized power mean curvature flow
Giovanni Bellettini, Shokhrukh Yu. Kholmatov
Motivated by a conjecture of De Giorgi, we consider the Almgren-Taylor-Wang scheme for mean curvature flow, where the volume penalization is replaced by a term of the form \[ \int_…
Minimizing movements for forced anisotropic curvature flow of droplets
Shokhrukh Yu. Kholmatov
We study forced anisotropic curvature flow of droplets on an inhomogeneous horizontal hyperplane. As in [Bellettini, Kholmatov: J. Math. Pures Appl. (2018)] we establish the existe…
On the minimality of the Winterbottom shape
Shokhrukh Yu. Kholmatov
In this short note we prove that the Winterbottom shape [Winterbottom: Acta Metallurgica (1967)] is a volume-constraint minimizer of the corresponding anisotropic capillary functio…
Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions
Giovanni Bellettini, Shokhrukh Kholmatov, Firdavsjon Almuratov
We study the crystalline curvature flow of planar networks with a single hexagonal anisotropy. After proving the local existence of a classical solution for a rather large class of…