Translating graphs by mean curvature flow
By Leili Shahriyari. 2012
73 citations recorded by the source corpus.
The aim of this work is studying translating graphs by mean curvature flow in $$\mathbb {R}^3$$R3. We prove non-existence of complete translating graphs over bounded domains in $$\mathbb {R}^2$$R2. Furthermore, we show that there are only three types of complete translating graphs in $$\mathbb {R}^3$$R3; entire graphs, graphs between two vertical planes, and graphs in one side of a plane. In the last two types, graphs are asymptotic to planes next to their boundaries. We also prove stability of translating graphs and then we obtain a pointwise curvature bound for translating graphs in $$\mathbb {R}^3$$R3.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e3bf52fc11bd74ffe547b19f3720a5b8df565fd9
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Mean Curvature Flow Solitons in the Presence of Conformal Vector Fields (2017, background): “This notion of translating soliton has been extensively studied in Euclidean spaces, see for instance [29], [4], [14], [38], [39], [41], [45], [48], [49] only to quote a few examples of the vast literature on the subject.”
- Complete translating solitons to the mean curvature flow in ℝ3 with nonnegative mean curvature (2020, unknown): “For two dimensional graphs, such curvature estimates follow immediately from the work of Leon Simon [31], see also [29].”
- Translating solitons of the mean curvature flow (2015, background): “Hence, the notion of L-stability in [21] is just the usual stability notion for oriented minimal hypersurfaces.”