TY - JOUR
T1 - Mean Curvature Ow of Graphs in Σ_{1} × Σ_{2}
JO - Journal of Partial Differential Equations
VL - 3
SP - 255
EP - 265
PY - 2003
DA - 2003/08
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5423.html
KW - Mean curvature flow
KW - m-dimensional graphs
AB - Let Σ_1 and Σ_2 be m and n dimensional Riemannian manifolds of constant curvature respectively. We assume that w is a unit constant m-form in Σ_1 with respect to which Σ_0 is a graph. We set v = 〈e_1 ∧ … ∧ e_m, 〉), where {e_1, …, e_m} is a normal frame on Σ_t. Suppose that Σ_0 has bounded curvature. If v(x, 0) ≥ v0 > \frac{\sqrt{p}}{2} for all x, then the mean curvature flow has a global solution F under some suitable conditions on the curvatrue of Σ_1 and Σ_2.