TY - GEN
A1 - Chuanxi Wu
A1 - Daping Tian
A1 - Guanghan Li
PB - National Academy of Sciences of Armenia
N2 - In this paper, we consider the $m^{\th}$ mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term. Under the assumption that the initial hypersurface is suitably pinched, we show that the flow may shrink to a point in finite time if the forcing term is small, or exist for all time and expand to infinity if the forcing term is large enough. The flow can also converge to a round sphere for some special forcing term and initial hypersurface. Furthermore, the normalization of the flow is carried out so that long time existence and convergence of the rescaled flow are studied. Our work extends Schulze's flow by powers of the mean curvature and Cabezas-Rivas and Sinestrari's volume-preserving flow by powers of the $m^{\th}$ mean curvature.
L1 - http://arar.sci.am/Content/13240/file_0.pdf
L2 - http://arar.sci.am/Content/13240
KW - Partial differential equations
KW - Differential geometry
T1 - Forced Flow by Powers of the $\emph{m}^{\th}$ Mean Curvature
UR - http://arar.sci.am/dlibra/docmetadata?id=13240
ER -