Volume 16, Issue 3
Mean Curvature Ow of Graphs in Σ1 × Σ2

Jiayu Li & Ye Li

J. Part. Diff. Eq., 16 (2003), pp. 255-265.

Published online: 2003-08

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  • Abstract
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.
  • Keywords

Mean curvature flow m-dimensional graphs

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@Article{JPDE-16-255, author = {}, title = {Mean Curvature Ow of Graphs in Σ1 × Σ2}, journal = {Journal of Partial Differential Equations}, year = {2003}, volume = {16}, number = {3}, pages = {255--265}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5423.html} }
TY - JOUR T1 - Mean Curvature Ow of Graphs in Σ1 × Σ2 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.
Jiayu Li & Ye Li . (2019). Mean Curvature Ow of Graphs in Σ1 × Σ2. Journal of Partial Differential Equations. 16 (3). 255-265. doi:
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